Chapter 1 Resource Masters - Math Problem Solvingjaeproblemsolving.weebly.com/uploads/5/1/9/6/... · ©Glencoe/McGraw-Hill iv Glencoe Geometry Teacher’s Guide to Using the Chapter

Chapter 1Resource Masters

Geometry

Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks.

Study Guide and Intervention Workbook 0-07-860191-6Skills Practice Workbook 0-07-860192-4Practice Workbook 0-07-860193-2Reading to Learn Mathematics Workbook 0-07-861061-3

ANSWERS FOR WORKBOOKS The answers for Chapter 1 of these workbookscan be found in the back of this Chapter Resource Masters booklet.

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Geometry. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027

ISBN: 0-07-846589-3 GeometryChapter 1 Resource Masters

1 2 3 4 5 6 7 8 9 10 009 11 10 09 08 07 06 05 04 03

© Glencoe/McGraw-Hill iii Glencoe Geometry

Contents

Vocabulary Builder . . . . . . . . . . . . . . . . vii

Lesson 1-1Study Guide and Intervention . . . . . . . . . . . 1–2Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 3Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Reading to Learn Mathematics . . . . . . . . . . . . 5Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Lesson 1-2Study Guide and Intervention . . . . . . . . . . . 7–8Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . 9Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Reading to Learn Mathematics . . . . . . . . . . . 11Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Lesson 1-3Study Guide and Intervention . . . . . . . . . 13–14Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 15Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Reading to Learn Mathematics . . . . . . . . . . . 17Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 18




Chapter 1 AssessmentChapter 1 Test, Form 1 . . . . . . . . . . . . . . 37–38Chapter 1 Test, Form 2A . . . . . . . . . . . . . 39–40Chapter 1 Test, Form 2B . . . . . . . . . . . . . 41–42Chapter 1 Test, Form 2C . . . . . . . . . . . . . 43–44Chapter 1 Test, Form 2D . . . . . . . . . . . . . 45–46Chapter 1 Test, Form 3 . . . . . . . . . . . . . . 47–48Chapter 1 Open-Ended Assessment . . . . . . . 49Chapter 1 Vocabulary Test/Review . . . . . . . . 50Chapter 1 Quizzes 1 & 2 . . . . . . . . . . . . . . . . 51Chapter 1 Quizzes 3 & 4 . . . . . . . . . . . . . . . . 52Chapter 1 Mid-Chapter Test . . . . . . . . . . . . . 53Chapter 1 Cumulative Review . . . . . . . . . . . . 54Chapter 1 Standardized Test Practice . . . 55–56

Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1

ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A29

© Glencoe/McGraw-Hill iv Glencoe Geometry

Teacher’s Guide to Using theChapter 1 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 1 Resource Masters includes the core materials neededfor Chapter 1. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theGeometry TeacherWorks CD-ROM.

Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

WHEN TO USE Give these pages tostudents before beginning Lesson 1-1.Encourage them to add these pages to theirGeometry Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.

Study Guide and InterventionEach lesson in Geometry addresses twoobjectives. There is one Study Guide andIntervention master for each objective.

WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.

WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.

Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.

WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.

WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.

© Glencoe/McGraw-Hill v Glencoe Geometry

Assessment OptionsThe assessment masters in the Chapter 1Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions

and is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-response Bonus question.

• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed throughtheir study of Geometry. It can also beused as a test. This master includes free-response questions.

• The Standardized Test Practice offerscontinuing review of geometry conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and short-responsequestions. Bubble-in and grid-in answersections are provided on the master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questionsthat appear in the Student Edition onpages 58–59. This improves students’familiarity with the answer formats theymay encounter in test taking.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided forthe assessment masters in this booklet.

Reading to Learn MathematicsVocabulary Builder

NAME ______________________________________________ DATE ____________ PERIOD _____

11

© Glencoe/McGraw-Hill vii Glencoe Geometry

Voca

bula

ry B

uild

erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 1.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Geometry Study Notebook to review vocabulary at the end of the chapter.

Vocabulary Term Found on Page Definition/Description/Example

acute angle

adjacent angles

uh·JAY·suhnt

angle

angle bisector

collinear

koh·LIN·ee·uhr

complementary angles

congruent

kuhn·GROO·uhnt

coplanar

koh·PLAY·nuhr

line segment

linear pair

(continued on the next page)

© Glencoe/McGraw-Hill viii Glencoe Geometry

Vocabulary Term Found on Page Definition/Description/Example

midpoint

obtuse angle

perimeter

perpendicular lines

polygon

PAHL·ee·gahn

ray

right angle

segment bisector

supplementary angles

vertical angles

Reading to Learn MathematicsVocabulary Builder (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

11

Study Guide and InterventionPoints, Lines, and Planes

NAME ______________________________________________ DATE ____________ PERIOD _____

1-11-1

© Glencoe/McGraw-Hill 1 Glencoe Geometry

Less

on

1-1

Name Points, Lines, and Planes In geometry, a point is a location, a line containspoints, and a plane is a flat surface that contains points and lines. If points are on the sameline, they are collinear. If points on are the same plane, they are coplanar.

Use the figure to name each of the following.

a. a line containing point A

The line can be named as �. Also, any two of the three points on the line can be used to name it.

AB��, AC��, or BC��

b. a plane containing point D

The plane can be named as plane N or can be named using three noncollinear points in the plane, such as plane ABD, plane ACD, and so on.

Refer to the figure.

1. Name a line that contains point A.

2. What is another name for line m ?

3. Name a point not on AC��.

4. Name the intersection of AC�� and DB��.

5. Name a point not on line � or line m .

Draw and label a plane Q for each relationship.

6. AB�� is in plane Q.

7. ST�� intersects AB�� at P.

8. Point X is collinear with points A and P.

9. Point Y is not collinear with points T and P.

10. Line � contains points X and Y.

�Q

AB

S

P

TY

X

�

Pm

AB

EC

D

�

N

AB

C

DExampleExample

ExercisesExercises


Points, Lines, and Planes in Space Space is a boundless, three-dimensional set ofall points. It contains lines and planes.

a. How many planes appear in the figure?

There are three planes: plane N , plane O, and plane P.

b. Are points A, B, and D coplanar?

Yes. They are contained in plane O.


1. Name a line that is not contained in plane N.

2. Name a plane that contains point B.

3. Name three collinear points.


4. How many planes are shown in the figure?

5. Are points B, E, G, and H coplanar? Explain.

6. Name a point coplanar with D, C, and E.

Draw and label a figure for each relationship.

7. Planes M andN intersect in HJ��.

8. Line r is in plane N , line s is in plane M, and lines r and sintersect at point J.

9. Line t contains point H and line t does not lie in plane M orplane N.

N

Ms

t

r

HJ

A B

CD

EF

G HI

J

N

A

C

B

D

E

NO

P

AB

CD

Study Guide and Intervention (continued)

Points, Lines, and Planes

NAME ______________________________________________ DATE ____________ PERIOD _____

1-11-1

ExampleExample

ExercisesExercises

Skills PracticePoints, Lines, and Planes

NAME ______________________________________________ DATE ____________ PERIOD _____

1-11-1


Less

on

1-1


1. Name a line that contains point D.

2. Name a point contained in line n.

3. What is another name for line p?

4. Name the plane containing lines n and p.


5. Point K lies on RT��. 6. Plane J contains line s.

7. YP�� lies in plane B and contains 8. Lines q and f intersect at point Zpoint C, but does not contain point H. in plane U.



10. How many of the planes contain points F and E?

11. Name four points that are coplanar.

12. Are points A, B, and C coplanar? Explain.

WA

B

E

C

DF

U

q f

Z

HP

B

CY

J

sTR

K

G

n

A BD

C

p



1. Name a line that contains points T and P.

2. Name a line that intersects the plane containing points Q, N, and P.

3. Name the plane that contains TN�� and QR��.


4. AK�� and CG�� intersect at point M 5. A line contains L(�4, �4) and M(2, 3). Line in plane T. q is in the same coordinate plane but does

not intersect LM��. Line q contains point N.




8. Are points N, R, S, and W coplanar? Explain.

VISUALIZATION Name the geometric term(s) modeled by each object.

9. 10. 11.

12. a car antenna 13. a library card

strings

tip of pinSTOP

A M N

PW S

X R

QT

L

M

N

q

x

y

O

KT

M

C

GA

S

j

g

hT

M

N

Q

R

P

Practice Points, Lines, and Planes

NAME ______________________________________________ DATE ____________ PERIOD _____

1-11-1

Reading to Learn MathematicsPoints, Lines, and Planes

NAME ______________________________________________ DATE ____________ PERIOD _____

1-11-1


Less

on

1-1

Pre-Activity Why do chairs sometimes wobble?

Read the introduction to Lesson 1-1 at the top of page 6 in your textbook.

• Find three pencils of different lengths and hold them upright on yourdesk so that the three pencil points do not lie along a single line. Can youplace a flat sheet of paper or cardboard so that it touches all three pencilpoints?

• How many ways can you do this if you keep the pencil points in the sameposition?

• How will your answer change if there are four pencil points?

Reading the Lesson

1. Complete each sentence.

a. Points that lie on the same lie are called points.

b. Points that do not lie in the same plane are called points.

c. There is exactly one through any two points.

d. There is exactly one through any three noncollinear points.

2. Refer to the figure at the right. Indicate whether each statement is true or false.

a. Points A, B, and C are collinear.

b. The intersection of plane ABC and line m is point P.

c. Line � and line m do not intersect.

d. Points A, P,and B can be used to name plane U.

e. Line � lies in plane ACB.

3. Complete the figure at the right to show the following relationship: Lines �, m, and n are coplanar and lie in plane Q. Lines � and m intersect at point P. Line nintersects line m at R, but does not intersect line �.

Helping You Remember

4. Recall or look in a dictionary to find the meaning of the prefix co-. What does this prefixmean? How can it help you remember the meaning of collinear?

Qn

m

�P

R

U

m

�PC

D

B

A


Points and Lines on a MatrixA matrix is a rectangular array of rows and columns. Points andlines on a matrix are not defined in the same way as in Euclideangeometry. A point on a matrix is a dot, which can be small orlarge. A line on a matrix is a path of dots that “line up.” Betweentwo points on a line there may or may not be other points. Threeexamples of lines are shown at the upper right. The broad line canbe thought of as a single line or as two narrow lines side by side.

Dot-matrix printers for computers used dots to form characters.The dots are often called pixels. The matrix at the right showshow a dot-matrix printer might print the letter P.

Draw points on each matrix to create the given figures.

1. Draw two intersecting lines that have 2. Draw two lines that cross but have four points in common. no common points.

3. Make the number 0 (zero) so that it 4. Make the capital letter O so that itextends to the top and bottom sides extends to each side of the matrix.of the matrix.

5. Using separate grid paper, make dot designs for several other letters. Which were theeasiest and which were the most difficult?

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

1-11-1

Study Guide and InterventionLinear Measure and Precision

NAME ______________________________________________ DATE ____________ PERIOD _____

1-21-2


Less

on

1-2

Measure Line Segments A part of a line between two endpoints is called a linesegment. The lengths of M�N� and R�S� are written as MN and RS. When you measure asegment, the precision of the measurement is half of the smallest unit on the ruler.

Find the length of M�N�.

The long marks are centimeters, and theshorter marks are millimeters. The length of M�N� is 3.4 centimeters. The measurement is accurate to within 0.5 millimeter, so M�N� isbetween 3.35 centimeters and 3.45centimeters long.

1cm 2 3 4

M N

Find the length of R�S�.

The long marks are inches and the short marks are quarter inches. The length of R�S�is about 1�

34� inches. The measurement is

accurate to within one half of a quarter inch,

or �18� inch, so R�S� is between 1�

58� inches and

1�78� inches long.

1 2in.

R S

Example 1Example 1 Example 2Example 2

ExercisesExercises

Find the length of each line segment or object.

1. 2.

3. 4.

Find the precision for each measurement.

5. 10 in. 6. 32 mm 7. 44 cm

8. 2 ft 9. 3.5 mm 10. 2�12� yd

1cm 2 31 2in.

1in.

S T

1cm 2 3

A B


Calculate Measures On PQ��, to say that point M is between points P and Q means P, Q, and M are collinear and PM � MQ � PQ.

On AC��, AB � BC � 3 cm. We can say that the segments arecongruent, or A�B� � B�C�. Slashes on the figure indicate whichsegments are congruent.

AB

C

QMP


Linear Measure and Precision

NAME ______________________________________________ DATE ____________ PERIOD _____

1-21-2

Find EF.

Calculate EF by adding ED and DF.

ED � DF � EF1.2 � 1.9 � EF

3.1 � EF

Therefore, E�F� is 3.1 centimeters long.

E1.2 cm 1.9 cm

FD

Find x and AC.

B is between A and C.

AB � BC � ACx � 2x � 2x � 5

3x � 2x � 5x � 5

AC � 2x � 5 � 2(5) � 5 � 15

A x 2x CB

2x � 5


ExercisesExercises

Find the measurement of each segment. Assume that the art is not drawn to scale.

1. R�T� 2. B�C�

3. X�Z� 4. W�X�

Find x and RS if S is between R and T.

5. RS � 5x, ST � 3x, and RT � 48. 6. RS � 2x, ST � 5x � 4, and RT � 32.

7. RS � 6x, ST �12, and RT � 72. 8. RS � 4x, R�S� � S�T�, and RT � 24.

Use the figures to determine whether each pair of segments is congruent.

9. A�B� and C�D� 10. X�Y� and Y�Z�X

Y Z

3x � 5 5x � 1

9x2

A D

CB

11 cm

11 cm

5 cm5 cm

W Y

6 cm

XX ZY

3–4 in.31–

2 in.

A C

6 in.

23–4 in. BR T

2.0 cm 2.5 cm

S

Skills PracticeLinear Measure and Precision

NAME ______________________________________________ DATE ____________ PERIOD _____

1-21-2


Less

on

1-2


1. 2.


3. 40 feet 4. 12 centimeters 5. 9�12� inches

Find the measurement of each segment.

6. N�Q� 7. A�C� 8. G�H�

Find the value of the variable and YZ if Y is between X and Z.

9. XY � 5p, YZ � p, and XY � 25 10. XY � 12, YZ � 2g, and XZ � 28

11. XY � 4m, YZ � 3m, and XZ � 42 12. XY � 2c � 1, YZ � 6c, and XZ � 81


13. B�E�, C�D� 14. M�P�, N�P� 15. W�X�, W�Z�

Y Z

WX

9 ft

5 ft 5 ft

N

P

M 10 yd

12 yd

12 ydE D

CB

5 m

2 m

3 m 3 m

F 9.7 mm HG

15 mmA4.9 cm 5.2 cm

CBQ1in. 11–

4 in.

NP

1 2in.

1cm 2 3 54



1. 2.


3. 120 meters 4. 7�14� inches 5. 30.0 millimeters

Find the measurement of each segment.

6. P�S� 7. A�D� 8. W�X�

Find the value of the variable and KL if K is between J and L.

9. JK � 6r, KL � 3r, and JL � 27 10. JK � 2s, KL � s � 2, and JL � 5s � 10


11. T�U�, S�W� 12. A�D�, B�C� 13. G�F�, F�E�

14. CARPENTRY Jorge used the figure at the right to make a pattern for a mosaic he plans to inlay on a tabletop. Name all of the congruent segments in the figure.

D

A

BF

E C

G H

EF

5x

6xD C

BA

12.9 in.

12.7 in.

W

T S

U

2 ft

2 ft

3 ft

3 ft

W 89.6 cm YX

100 cmA

11–4 in.23–

8 in.

DCP4.7 cm18.4 cm

SQ

1cm 2 3 541 2in.

E F

Practice Linear Measure and Precision

NAME ______________________________________________ DATE ____________ PERIOD _____

1-21-2

Reading to Learn MathematicsLinear Measure and Precision

NAME ______________________________________________ DATE ____________ PERIOD _____

1-21-2


Less

on

1-2

Pre-Activity Why are units of measure important?


• The basic unit of length in the metric system is the meter. How manymeters are there in one kilometer?

• Do you think it would be easier to learn the relationships between thedifferent units of length in the customary system (used in the UnitedStates) or in the metric system? Explain your answer.

Reading the Lesson

1. Explain the difference between a line and a line segment and why one of these can bemeasured, while the other cannot.

2. What is the smallest length marked on a 12-inch ruler?What is the smallest length marked on a centimeter ruler?

3. Find the precision of each measurement.a. 15 cmb. 15.0 cm

4. Refer to the figure at the right. Which one of the following statements is true? Explain your answer.A�B� � C�D� A�B� � C�D�

5. Suppose that S is a point on V�W� and S is not the same point as V or W. Tell whethereach of the following statements is always, sometimes, or never true.a. VS � SWb. S is between V and W.c. VS � VW � SW


6. A good way to remember terms used in mathematics is to relate them to everyday wordsyou know. Give three words that are used outside of mathematics that can help youremember that there are 100 centimeters in a meter.

A

B

4.5 cm 4.5 cm

DC


Points Equidistant from SegmentsThe distance from a point to a segment is zero if the point is on the segment. Otherwise, it is the length of the shortest segment from the point to the segment.

A figure is a locus if it is the set of all points that satisfy

a set of conditions. The locus of all points that are �14� inch

from the segment AB is shown by two dashed segments with semicircles at both ends.

1. Suppose A, B, C, and D are four different points, and consider the locus of all points x units from A�B� and x units from C�D�. Use any unit you findconvenient. The locus can take different forms. Sketch at least threepossibilities. List some of the things that seem to affect the form of the locus.

2. Conduct your own investigation of the locus of pointsequidistant from two segments. Describe your results on aseparate sheet of paper.

A BC D

P Q

R S

A

B

C

D

X

Y

A B

C DX Y

A B

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

1-21-2

Study Guide and InterventionDistance and Midpoints

NAME ______________________________________________ DATE ____________ PERIOD _____

1-31-3


Less

on

1-3

Distance Between Two Points

Distance on a Number Line Distance in the Coordinate Plane

AB � |b � a | or |a � b |x

y

OC(1, –1)

A(–2, –1)

B(1, 3)

Pythagorean Theorem:

a2 � b2 � c2

Distance Formula:

d � �(x2 ��x1)2 �� (y2 �� y1)2�

A B

a b

Find AB.

AB � |(�4) � 2|� |� 6|� 6

�5 �4 �3 �2 �1 0 1 2 3

A B

Find the distance between A(�2, �1) and B(1, 3).


Pythagorean Theorem

(AB)2 � (AC)2 � (BC)2

(AB)2 � (3)2 � (4)2

(AB)2 � 25

AB � �25�� 5

Distance Formula

d � �(x2 ��x1)2 �� (y2 �� y1)2�AB � �(1 � (��2))2�� (3 �� (�1))�2�AB � �(3)2 �� (4)2�

� �25�� 5

Use the number line to find each measure.

1. BD 2. DG

3. AF 4. EF

5. BG 6. AG

7. BE 8. DE

Use the Pythagorean Theorem to find the distance between each pair of points.

9. A(0, 0), B(6, 8) 10. R(�2, 3), S(3, 15)

11. M(1, �2), N(9, 13) 12. E(�12, 2), F(�9, 6)

Use the Distance Formula to find the distance between each pair of points.

13. A(0, 0), B(15, 20) 14. O(�12, 0), P(�8, 3)

15. C(11, �12), D(6, 2) 16. E(�2, 10), F(�4, 3)

–10 –8 –6 –4 –2 0 2 4 6 8

A B C D E F G

ExercisesExercises


Midpoint of a Segment

Midpoint on a If the coordinates of the endpoints of a segment are a and b,

Number Line then the coordinate of the midpoint of the segment is �a �2

b�.

Midpoint on a If a segment has endpoints with coordinates (x1, y1) and (x2, y2),

Coordinate Plane then the coordinates of the midpoint of the segment are ��x1 �

2x2�, �

y1 �

2y2��.

Find the coordinate of the midpoint of P�Q�.

The coordinates of P and Q are �3 and 1.

If M is the midpoint of P�Q�, then the coordinate of M is ��32� 1� � �

�22� or �1.

M is the midpoint of P�Q� for P(�2, 4) and Q(4, 1). Find thecoordinates of M.

M � ��x1 �

2x2�, �

y1 �

2y2�� 2

2� 4�, �

4 �2

1�� or (1, 2.5)

Use the number line to find the coordinate of the midpoint of each segment.

1. C�E� 2. D�G�

3. A�F� 4. E�G�

5. A�B� 6. B�G�

7. B�D� 8. D�E�

Find the coordinates of the midpoint of a segment having the given endpoints.

9. A(0, 0), B(12, 8) 10. R(�12, 8), S(6, 12)

11. M(11, �2), N(�9, 13) 12. E(�2, 6), F(�9, 3)

13. S(10, �22), T(9, 10) 14. M(�11, 2), N(�19, 6)

–10 –8 –6 –4 –2 0 2 4 6 8

A B C D E F G

–3 –2 –1 0 1 2

P Q


Distance and Midpoints

NAME ______________________________________________ DATE ____________ PERIOD _____

1-31-3

Example 1Example 1

Example 2Example 2

ExercisesExercises

Skills PracticeDistance and Midpoints

NAME ______________________________________________ DATE ____________ PERIOD _____

1-31-3


Less

on

1-3


1. LN 2. JL

3. KN 4. MN


5. 6.

7. K(2, 3), F(4, 4) 8. C(�3, �1), Q(�2, 3)


9. Y(2, 0), P(2, 6) 10. W(�2, 2), R(5, 2)

11. A(�7, �3), B(5, 2) 12. C(�3, 1), Q(2, 6)


13. D�E� 14. B�C�

15. B�D� 16. A�D�


17. T(3, 1), U(5, 3) 18. J(�4, 2), F(5, �2)

Find the coordinates of the missing endpoint given that P is the midpoint of N�Q�.

19. N(2, 0), P(5, 2) 20. N(5, 4), P(6, 3) 21. Q(3, 9), P(�1, 5)

–6 –4 –2 0 2 4 6 8 10 12

A B C D E

x

y

O

D

S

x

y

O

F

G

–6 –4 –2 0 2 4 6 8 10

J K L M N



1. VW 2. TV

3. ST 4. SV


5. 6.


7. L(�7, 0), Y(5, 9) 8. U(1, 3), B(4, 6)


9. R�T� 10. Q�R�

11. S�T� 12. P�R�


13. K(�9, 3), H(5, 7) 14. W(�12, �7), T(�8, �4)

Find the coordinates of the missing endpoint given that E is the midpoint of D�F�.

15. F(5, 8), E(4, 3) 16. F(2, 9), E(�1, 6) 17. D(�3, �8), E(1, �2)

18. PERIMETER The coordinates of the vertices of a quadrilateral are R(�1, 3), S(3, 3),T(5, �1), and U(�2, �1). Find the perimeter of the quadrilateral. Round to the nearest tenth.

–6 –4–10 –8 –2 0 2 4 6

P Q R S T

x

y

O

E

S

x

y

OM

Z

–6 –4–10 –8 –2 0 2 4 6 8

S T U V W

Practice Distance and Midpoints

NAME ______________________________________________ DATE ____________ PERIOD _____

1-31-3

Reading to Learn MathematicsDistance and Midpoints

NAME ______________________________________________ DATE ____________ PERIOD _____

1-31-3


Less

on

1-3

Pre-Activity How can you find the distance between two points without a ruler?


• Look at the triangle in the introduction to this lesson. What is the specialname for A�B� in this triangle?

• Find AB in this figure. Write your answer both as a radical and as adecimal number rounded to the nearest tenth.

Reading the Lesson

1. Match each formula or expression in the first column with one of the names in thesecond column.

a. d � �(x2 ��x1)2 �� ( y2 �� y1)2� i. Pythagorean Theorem

b. �a �

2b

� ii. Distance Formula in the Coordinate Plane

c. XY � |a � b| iii. Midpoint of a Segment in the Coordinate Plane

d. c2 � a2 � b2 iv. Distance Formula on a Number Line

e. ��x1 �

2x2

�, �y1 �

2y2

�� v. Midpoint of a Segment on a Number Line

2. Fill in the steps to calculate the distance between the points M(4, �3) and N(�2, 7).

Let (x1, y1) � (4, �3). Then (x2, y2) � ( , ).

d � ��( � )2 � ( � )2

MN � ��( � )2 � ( � )2

MN � ��( )2 � ( )2

MN � ��

MN � ��Find a decimal approximation for MN to the nearest hundredth.


3. A good way to remember a new formula in mathematics is to relate it to one you alreadyknow. If you forget the Distance Formula, how can you use the Pythagorean Theorem tofind the distance d between two points on a coordinate plane?


Lengths on a GridEvenly-spaced horizontal and vertical lines form a grid.

You can easily find segment lengths on a grid if the endpoints are grid-lineintersections. For horizontal or verticalsegments, simply count squares. For diagonal segments, use the PythagoreanTheorem (proven in Chapter 7). This theorem states that in any right triangle,if the length of the longest side (the sideopposite the right angle) is c and the twoshorter sides have lengths a and b, then c2 � a2 � b2.

Find the measure of E�F� on the grid at the right. Locate a right triangle with E�F� as its longest side.

EF � �22 � 5�2� � �29� � 5.4 units

Find each measure to the nearest tenth of a unit.

1. I�J� 2. M�N� 3. R�S� 4. Q�S�

5. I�K� 6. J�K� 7. L�M� 8. L�N�

Use the grid above. Find the perimeter of each triangle to the nearest tenth of a unit.

9. � ABC 10. �QRS 11. � DEF 12. � LMN

13. Of all the segments shown on the 14. On the grid, 1 unit � 0.5 cm. How can the grid, which is longest? What is its answers above be used to find the measures length? in centimeters?

15. Use your answer from exercise 8 to 16. Use a centimeter ruler to find the perimeter calculate the length of segment LN of triangle IJK to the nearest tenth of a in centimeters. Check by measuring centimeter.with a centimeter ruler.

E

2

5 F

A

B

F

I

J

K N M

C

D

E

S

R

Q

L

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

1-31-3

ExampleExample

Study Guide and InterventionAngle Measure

NAME ______________________________________________ DATE ____________ PERIOD _____

1-41-4


Less

on

1-4

Measure Angles If two noncollinear rays have a common endpoint, they form an angle. The rays are the sides of the angle.The common endpoint is the vertex. The angle at the right can be named as �A, �BAC, �CAB, or �1.

A right angle is an angle whose measure is 90. An acute anglehas measure less than 90. An obtuse angle has measure greater than 90 but less than 180.

A C

B

1

a. Name all angles that have R as avertex.Three angles are �1, �2, and �3. Forother angles, use three letters to namethem: �SRQ, �PRT, and �SRT.

b. Name the sides of �1.

RS��, RP��

S R T

PQ

1 2 3

Measure each angle andclassify it as right, acute, or obtuse.

a. �ABDUsing a protractor, m�ABD � 50.50 � 90, so �ABD is an acute angle.

b. �DBCUsing a protractor, m�DBC � 115.180 � 115 � 90, so �DBC is an obtuseangle.

c. �EBCUsing a protractor, m�EBC � 90.�EBC is a right angle.

BA

D E

C


ExercisesExercises


1. Name the vertex of �4.

2. Name the sides of �BDC.

3. Write another name for �DBC.

Measure each angle in the figure and classify it as right,acute, or obtuse.

4. �MPR

5. �RPN

6. �NPS

P

NM

R

S

C

BA

12

34

D


Congruent Angles Angles that have the same measure are congruent angles. A ray that divides an angle into two congruent angles is called an angle bisector. In the figure, PN�� is the angle bisector of �MPR. Point N lies in the interior of �MPR and �MPN � �NPR.

Refer to the figure above. If m�MPN � 2x � 14 and m�NPR � x � 34, find x and find m�MPR.Since PN�� bisects �MPR, �MPN � �NPR, or m�MPN � m�NPR.

2x � 14 � x � 34 m�NPR � (2x � 14) � (x � 34)2x � 14 � x � x � 34 � x � 54 � 54

x � 14 � 34 � 108x � 14 � 14 � 34 � 14

x � 20

QS�� bisects �PQT, and QP�� and QR�� are opposite rays.

1. If m�PQT � 60 and m�PQS � 4x � 14, find the value of x.

2. If m�PQS � 3x � 13 and m�SQT � 6x � 2, find m�PQT.

BA�� and BC�� are opposite rays, BF�� bisects �CBE, and BD�� bisects �ABE.

3. If m�EBF � 6x � 4 and m�CBF � 7x � 2, find m�EBC.

4. If m�1 � 4x � 10 and m�2 � 5x, find m�2.

5. If m�2 � 6y � 2 and m�1 � 8y � 14, find m�ABE.

6. Is �DBF a right angle? Explain.

BA C

F

ED

12 3

4

QP R

TS

P R

NM


Angle Measure

NAME ______________________________________________ DATE ____________ PERIOD _____

1-41-4

ExampleExample

ExercisesExercises

Skills PracticeAngle Measure

NAME ______________________________________________ DATE ____________ PERIOD _____

1-41-4


Less

on

1-4

For Exercises 1–12, use the figure at the right.

Name the vertex of each angle.

1. �4 2. �1

3. �2 4. �5

Name the sides of each angle.

5. �4 6. �5

7. �STV 8. �1

Write another name for each angle.

9. �3 10. �4

11. �WTS 12. �2

Measure each angle and classify it as right, acute,or obtuse.

13. �NMP 14. �OMN

15. �QMN 16. �QMO

ALGEBRA In the figure, BA�� and BC�� are opposite rays,BD�� bisects �EBC, and BF�� bisects �ABE.

17. If m�EBD � 4x � 16 and m�DBC � 6x � 4,find m�EBD.

18. If m�ABF � 7x � 8 and m�EBF � 5x � 10,find m�EBF.

B CA

FE

D

M NL

Q O

P

U

T

VW

S5 3

21

4


For Exercises 1–10, use the figure at the right.

Name the vertex of each angle.

1. �5 2. �3

3. �8 4. �NMP

Name the sides of each angle.

5. �6 6. �2

7. �MOP 8. �OMN

Write another name for each angle.

9. �QPR 10. �1

Measure each angle and classify it as right, acute,or obtuse.

11. �UZW 12. �YZW

13. �TZW 14. �UZT

ALGEBRA In the figure, CB�� and CD�� are opposite rays,CE�� bisects �DCF, and CG�� bisects �FCB.

15. If m�DCE � 4x � 15 and m�ECF � 6x � 5,find m�DCE.

16. If m�FCG � 9x � 3 and m�GCB � 13x � 9,find m�GCB.

17. TRAFFIC SIGNS The diagram shows a sign used to warn drivers of a school zone or crossing. Measure and classify each numbered angle. 2

1

B

C

G

F

ED

Z YT

U

V W

X

N

O

PQ

R

M12

8

3

54

6

7

Practice Angle Measure

NAME ______________________________________________ DATE ____________ PERIOD _____

1-41-4

Reading to Learn MathematicsAngle Measure

NAME ______________________________________________ DATE ____________ PERIOD _____

1-41-4


Less

on

1-4

Pre-Activity How big is a degree?

Read the introduction to Lesson 1-4 at the top of page 29 in your textbook.• A semicircle is half a circle. How many degrees are there in a

semicircle?• How many degrees are there in a quarter circle?

Reading the Lesson1. Match each description in the first column with one of the terms in the second column.

Some terms in the second column may be used more than once or not at all.a. a figure made up of two noncollinear rays with a 1. vertex

common endpoint 2. angle bisectorb. angles whose degree measures are less than 90 3. opposite raysc. angles that have the same measure 4. angled. angles whose degree measures are between 90 and 180 5. obtuse anglese. a tool used to measure angles 6. congruent anglesf. the common endpoint of the rays that form an angle 7. right anglesg. a ray that divides an angle into two congruent angles 8. acute angles

9. compass10. protractor

2. Use the figure to name each of the following.a. a right angleb. an obtuse anglec. an acute angled. a point in the interior of �EBCe. a point in the exterior of �EBAf. the angle bisector of �EBCg. a point on �CBEh. the sides of �ABFi. a pair of opposite raysj. the common vertex of all angles shown in the figurek. a pair of congruent anglesl. the angle with the greatest measure

Helping You Remember3. A good way to remember related geometric ideas is to compare them and see how they

are alike and how they are different. Give some similarities and differences betweencongruent segments and congruent angles.

B G

28�28�

A

EF

CD


Angle RelationshipsAngles are measured in degrees (�). Each degree of an angle is divid-ed into 60 minutes (�), and each minute of an angle is divided into 60 seconds ().

60� � 1�

60 � 1�

67�12�� 67�30�

70.4� � 70°24�

90� � 89°60�

Two angles are complementary if the sum of their measures is 90�.Find the complement of each of the following angles.

1. 35�15� 2. 27�16� 3. 15�54�

4. 29�18�22 5. 34�29�45 6. 87�2�3

Two angles are supplementary if the sum of their measures is 180�.Find the supplement of each of the following angles.

7. 120�18� 8. 84�12� 9. 110�2�

10. 45�16�24 11. 39�21�54 12. 129�18�36

13. 98�52�59 14. 9�2�32 15. 1�2�3

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

1-41-4

Study Guide and InterventionAngle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

1-51-5


Less

on

1-5

Pairs of Angles Adjacent angles are angles in the same plane that have a commonvertex and a common side, but no common interior points. Vertical angles are twononadjacent angles formed by two intersecting lines. A pair of adjacent angles whosenoncommon sides are opposite rays is called a linear pair.

Identify each pair of angles as adjacent angles, vertical angles,and/or as a linear pair.

ExampleExample

a.

�SRT and �TRU have a commonvertex and a common side, but nocommon interior points. They areadjacent angles.

c.

�6 and �5 are adjacent angles whosenoncommon sides are opposite rays.The angles form a linear pair.

D

CBA

5 6

RU

TS

b.

�1 and �3 are nonadjacent angles formedby two intersecting lines. They are verticalangles. �2 and �4 are also vertical angles.

d.

�A and �B are two angles whose measureshave a sum of 90. They are complementary.�F and �G are two angles whose measureshave a sum of 180. They are supplementary.

AB

FG

30�

60�

60�120�

N

RP

SM

14

32

ExercisesExercises

Identify each pair of angles as adjacent, vertical, and/or as a linear pair.

1. �1 and �2 2. �1 and �6

3. �1 and �5 4. �3 and �2

For Exercises 5–7, refer to the figure at the right.

5. Identify two obtuse vertical angles.

6. Identify two acute adjacent angles.

7. Identify an angle supplementary to �TNU.

8. Find the measures of two complementary angles if the difference in their measures is 18.

R S

NU

T

V

R

S

TU

V

P

Q5

432

1 6


Perpendicular Lines Lines, rays, and segments that form four right angles are perpendicular. The right angle symbol indicates that the lines are perpendicular. In the figure at the right, AC�� is perpendicular to BD��,or AC�� ⊥ BD��.

Find x so that D�Z� ⊥ P�Z�.If D�Z� ⊥ P�Z�, then m�DZP � 90.

m�DZQ � m�QZP � m�DZP Sum of parts � whole

(9x � 5) � (3x � 1) � 90 Substitution

12x � 6 � 90 Simplify.12x � 84 Subtract 6 from each side.

x � 7 Divide each side by 12.

1. Find x and y so that NR�� ⊥ MQ��.

2. Find m�MSN.

3. m�EBF � 3x � 10, m�DBE � x, and BD�� ⊥ BF��. Find x.

4. If m�EBF � 7y � 3 and m�FBC � 3y � 3, find y so that EB�� ⊥ BC��.

5. Find x, m�PQS, and m�SQR.

6. Find y, m�RPT, and m�TPW.

P

S

V

R

W

T(4y � 5)�

(2y � 5)�

Q R

P S3x �

(8x � 2)�

B CA

DE

F

M

N

R

S Q

P

x �5x �

(9y � 18)�

Z

D

P

Q(9x � 5)�

(3x � 1)�

B

CD

A


Angle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

1-51-5

ExampleExample

ExercisesExercises

Skills PracticeAngle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

1-51-5


Less

on

1-5

For Exercises 1–6, use the figure at the right and a protractor.

1. Name two acute vertical angles.

2. Name two obtuse vertical angles.

3. Name a linear pair.

4. Name two acute adjacent angles.

5. Name an angle complementary to �EKH.

6. Name an angle supplementary to �FKG.

7. Find the measures of an angle and its complement if one angle measures 18 degreesmore than the other.

8. The measure of the supplement of an angle is 36 less than the measure of the angle.Find the measures of the angles.

ALGEBRA For Exercises 9–10, use the figure at the right.

9. If m�RTS � 8x � 18, find x so that TR�� ⊥ TS��.

10. If m�PTQ � 3y � 10 and m�QTR � y, find y so that �PTR is a right angle.

Determine whether each statement can be assumed from the figure. Explain.

11. �WZU is a right angle.

12. �YZU and �UZV are supplementary.

13. �VZU is adjacent to �YZX.

ZX

W

V

Y

U

TP

QR

S

K

G

J

FE

H


For Exercises 1–4, use the figure at the right and a protractor.


2. Name a linear pair whose vertex is B.

3. Name an angle not adjacent to but complementary to �FGC.

4. Name an angle adjacent and supplementary to �DCB.

5. Two angles are complementary. The measure of one angle is 21 more than twice themeasure of the other angle. Find the measures of the angles.

6. If a supplement of an angle has a measure 78 less than the measure of the angle, whatare the measures of the angles?

ALGEBRA For Exercises 7–8, use the figure at the right.

7. If m�FGE � 5x � 10, find x so that FC�� ⊥ AE��.

8. If m�BGC � 16x � 4 and m�CGD � 2x � 13,find x so that �BGD is a right angle.

Determine whether each statement can be assumed from the figure. Explain.

9. �NQO and �OQP are complementary.

10. �SRQ and �QRP is a linear pair.

11. �MQN and �MQR are vertical angles.

12. STREET MAPS Darren sketched a map of the cross streets nearest to his home for his friend Miguel. Describe two different anglerelationships between the streets. Olive

Beac

on

Main

Q

O

P

RS

M

N

GF

AB

E

D

C

DA

E

HG

B C

F

Practice Angle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

1-51-5

Reading to Learn MathematicsAngle Relationships

NAME ______________________________________________ DATE ____________ PERIOD _____

1-51-5


Less

on

1-5

Pre-Activity What kinds of angles are formed when streets intersect?


• How many separate angles are formed if three lines intersect at a commonpoint? (Do not use an angle whose interior includes part of another angle.)

• How many separate angles are formed if n lines intersect at a commonpoint? (Do not count an angle whose interior includes part of another angle.)

Reading the Lesson1. Name each of the following in the figure at the right.

a. two pairs of congruent angles

b. a pair of acute vertical angles

c. a pair of obtuse vertical angles

d. four pairs of adjacent angles

e. two pairs of vertical angles

f. four linear pairs

g. four pairs of supplementary angles

2. Tell whether each statement is always, sometimes, or never true.

a. If two angles are adjacent angles, they form a linear pair.

b. If two angles form a linear pair, they are complementary.

c. If two angles are supplementary, they are congruent.

d. If two angles are complementary, they are adjacent.

e. When two perpendicular lines intersect, four congruent angles are formed.

f. Vertical angles are supplementary.

g. Vertical angles are complementary.

h. The two angles in a linear pair are both acute.

i. If two angles form a linear pair, one is acute and the other is obtuse.

3. Complete each sentence.

a. If two angles are supplementary and x is the measure of one of the angles, then themeasure of the other angle is .

b. If two angles are complementary and x is the measure of one of the angles, then themeasure of the other angle is .

Helping You Remember4. Look up the nonmathematical meaning of supplementary in your dictionary. How can

this definition help you to remember the meaning of supplementary angles?

65� 2 34

1


Curve StitchingThe star design at the right was created by a method known as curve stitching. Although the design appears to contain curves, it is made up entirely of line segments.

To begin the star design, draw a 60° angle. Mark eight equally-spaced points on each ray, and number the points as shown below. Then connect pairs of points that have the same number.

To make a complete star, make the same design in six 60° angles that have a common central vertex.

1. Complete the section of the star design above by connecting pairs of points that have the same number.

2. Complete the following design.

3. Create your own design. You may use several angles, and the angles may overlap.

1 2 3 4 5 6 7 8 9

11

11

12

13

14

15

16

17

18

19

1

2

3

4

5

6

7

8

9

12 13 14 15 16 17 18 19

8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 8

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

1-51-5

Study Guide and InterventionPolygons

NAME ______________________________________________ DATE ____________ PERIOD _____

1-61-6


Less

on

1-6

Polygons A polygon is a closed figure formed by a finite number of coplanar linesegments. The sides that have a common endpoint must be noncollinear and each sideintersects exactly two other sides at their endpoints. A polygon is named according to itsnumber of sides. A regular polygon has congruent sides and congruent angles. A polygoncan be concave or convex.

Name each polygon by its number of sides. Then classify it asconcave or convex and regular or irregular.

ExampleExample

a.

The polygon has 4 sides, so it is a quadrilateral.It is concave because part of D�E� or E�F� lies in theinterior of the figure. Because it is concave, itcannot have all its angles congruent and so it isirregular.

c.

The polygon has 5 sides, so it is a pentagon. It isconvex. All sides are congruent and all angles arecongruent, so it is a regular pentagon.

D F

G

E b.

The figure is not closed, so it isnot a polygon.

d.

The figure has 8 congruent sidesand 8 congruent angles. It isconvex and is a regular octagon.

H

J K

LI

ExercisesExercises

Name each polygon by its number of sides. Then classify it as concave or convexand regular or irregular.

1. 2. 3.

4. 5. 6.


Perimeter The perimeter of a polygon is the sum of the lengths of all the sides of thepolygon. There are special formulas for the perimeter of a square or a rectangle.

Write an expression or formula for the perimeter of each polygon.Find the perimeter.


Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

1-61-6

ExampleExample

a.

P � a � b � c� 3 � 4 � 5� 12 in.

b.

P � 4s� 4(5)� 20 cm

c.

P � 2� � 2w� 2(3) � 2(2)� 10 ft

3 ft

2 ft

�

�

w w

5 cm

5 cm 5 cm

5 cm

s

s

s s3 in.5 in.

4 in.

a

b

c

ExercisesExercises

Find the perimeter of each figure.

1. 2.

3. 4.

Find the length of each side of the polygon for the given perimeter.

5. P � 96 6. P � 48x

x

2x

x � 2

rectangle

2x

x

1 cm

24 yd

19 yd

12 yd 14 yd

27 yd

square

5.5 ft

3.5 cm

3 cm2.5 cm

Skills PracticePolygons

NAME ______________________________________________ DATE ____________ PERIOD _____

1-61-6


Less

on

1-6

Name each polygon by its number of sides and then classify it as convex orconcave and regular or irregular.

1. 2. 3.

4. 5. 6.


7. 8. 9.

COORDINATE GEOMETRY Find the perimeter of each polygon.

10. triangle ABC with vertices A(3, 5), B(3, 1), and C(0, 1)

11. quadrilateral QRST with vertices Q(�3, 2), R(1, 2), S(1, �4), and T(�3, �4)

12. quadrilateral LMNO with vertices L(�1, 4), M(3, 4), N(2, 1), and O(�2, 1)

ALGEBRA Find the length of each side of the polygon for the given perimeter.

13. P � 104 millimeters 14. P � 84 kilometers 15. P � 88 feet4w � 1

w

10 in.

10 in.2 in. 2 in.

2 in.2 in.2 in. 2 in.

5 m2 m 3 m

6 m4 m

40 yd

20 yd

18 yd 20 yd


Name each polygon by its number of sides and then classify it as convex orconcave and regular or irregular.

1. 2. 3.


4. 5. 6.

COORDINATE GEOMETRY Find the perimeter of each polygon.

7. quadrilateral OPQR with vertices O(�3, 2), P(1, 5), Q(6, 4), and R(5, �2)

8. pentagon STUVW with vertices S(0, 0), T(3, �2), U(2, �5), V(�2, �5), and W(�3, �2)

ALGEBRA Find the length of each side of the polygon for the given perimeter.

9. P � 26 inches 10. P � 39 centimeters 11. P � 89 feet

SEWING For Exercises 12–13, use the following information.Jasmine plans to sew fringe around the scarf shown in the diagram.

12. How many inches of fringe does she need to purchase?

13. If Jasmine doubles the width of the scarf, how many inches of fringe will she need?

16 in.

4 in. 4 in.

16 in.

2x � 2

x � 9

5x � 4

3x � 5

2x � 3

6n � 8

n

14 cm

14 cm

4 cm

4 cm 6 cm6 cm

6 cm2 cm

32 mi

33 mi21 mi

7 mm

10 mm18 mm

18 mm

Practice Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

1-61-6

Reading to Learn MathematicsPolygons

NAME ______________________________________________ DATE ____________ PERIOD _____

1-61-6


Less

on

1-6

Pre-Activity How are polygons related to toys?


Name four different shapes that can each be formed by four sticks connected toform a closed figure. Assume you have sticks with a good variety of lengths.

Reading the Lesson

1. Tell why each figure is not a polygon.

a. b. c.

2. Name each polygon by its number of sides. Then classify it as convex or concave andregular or not regular.

a. b. c.

3. What is another name for a regular quadrilateral?

4. Match each polygon in the first column with the formula in the second column that canbe used to find its perimeter. (s represents the length of each side of a regular polygon.)

a. regular dodecagon i. P � 8s

b. square ii. P � 6s

c. regular hexagon iii. P � a � b � c

d. rectangle iv. P � 12s

e. regular octagon v. P � 2� � 2w

f. triangle vi. P � 4s


5. One way to remember the meaning of a term is to explain it to another person.How would you explain to a friend what a regular polygon is?


Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

1-61-6

Perimeter and Area of Irregular ShapesTwo formulas that are used frequently in mathematics are perimeter andarea of a rectangle.

Perimeter: P � 2� � 2wArea: A � �w, where � is the length and w is the width

However, many figures are combinations of two or more rectangles creatingirregular shapes. To find the area of an irregular shape, it helps to separatethe shape into rectangles, calculate the formula for each rectangle, then findthe sum of the areas.

Find the area of thefigure at the right.Separate the figure into two rectangles.

A � �wA1 � 9 2 A2 � 3 3

� 18 � 9

18 � 9 � 27

The area of the irregular shape is 27 m2.

Find the area and perimeter of each irregular shape.

1. 2.

3.4.

For Exercises 5–8, find the perimeter of the figures in Exercises 1–4.

5. 6. 7. 8.

9. Describe the steps you used to find the perimeter in Exercise 1.

9 ft

2 ft

3 ft

7 ft

6 ft

4 ft

8 cm

4 cm

2 cm

2 cm

4 cm

4 cm

6 cm

4 cm

9 m

26 m

6 m13 m

7 m

12 m

2 in.

4 in. 4 in.

1 in.

9 m

3 m

1

25 m

2 m

9 m

3 m

5 m

2 m

ExampleExample

Chapter 1 Test, Form 111


Ass

essm

ents

Write the letter for the correct answer in the blank at the right of each question.

1. Name the geometric shape modeled by a pinhole in a wall.A. line segment B. plane C. line D. point

For Questions 2–4, use the figure given at the right.

2. Which is another name for line �?A. AB�� B. BD��

C. C D. P

3. Name the intersection of lines � and m.A. A B. BC. C D. P

4. Name three points coplanar with point A.A. B, C, F B. E, F, GC. B, C, E D. B, D, G

5. Find the length of R�S�.A. 33 mm B. 34 mmC. 35 mm D. 36 mm

6. Find the precision for a measurement of 72 centimeters.A. 0.5 cm B. 0.1 cmC. 1 mm D. 0.5 mm

7. Find the length of B�C�.A. 12 cm B. 13 cmC. 25 cm D. 38 cm

8. Use the number line to find MN.A. �5 B. 1C. 5 D. 10

For Questions 9 and 10, use the figure given at the right.

9. Find the distance between points P and Q.A. 5 B. 7C. 9 D. 25

10. Find the coordinates of the midpoint of P�Q�.

A. �2, 3�12�� B. �0, 3�

12�� C. (0, 3) D. �3�

12�, 0�

x

y

O

P

Q

�5 �4 �3 �2 �1 0 1 2 3

M N

A C

25 cm

13 cm B

1cm 2 3 4

R S

�

P

m

AB

C

D

E

G

F

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

NAME DATE PERIOD

SCORE

NAME DATE PERIOD


Chapter 1 Test, Form 1 (continued)11

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

For Questions 11–13, use the figure at the right.

11. Which point is the vertex of all the angles in this figure?A. A B. BC. C D. E

12. What type of angle is �ABC?A. acute angle B. right angle C. obtuse angle D. straight angle

13. Which is true?A. m�EBF � 140 B. m�EBF � 90 C. m�EBF � 50 D. m�EBF � 40

14. For what value of x is �ATK � �MJS if m�ATK � 5x � 4 and m�MJS � 8x � 11?A. 29 B. 15 C. 10 D. 5


15. Which pair of angles are vertical angles?A. �RST, �TSU B. �RSX, �TSUC. �TSU, �USV D. �RSX, �XSW

16. Which angle is supplementary to �USV ?A. �TSU B. �VSW C. �RSV D. �WSR

17. Find x and y.A. x � 10, y � 12 B. x � 20, y � 7 C. x � 10, y � 8 D. x � 50, y � 40

For Questions 18–20, use the figures below.

18. Which figure is not a polygon?A. Figure A B. Figure B C. Figure C D. Figure D

19. Find the perimeter of the convex pentagon.A. 46 cm B. 50 cm C. 61 cm D. 72 cm

20. Suppose the length and width of the rectangle are doubled. What is itsperimeter?A. 120 cm B. 92 cm C. 76 cm D. 46 cm

Bonus Each side of a square is 2x � 6 yards long. If the perimeter of the square is 72 yards what is the value of x?

8 cm

8 cm

8 cm

4 cm

15 cm15 cm

18 cm

18 cm

25 cm

15 cm

8 cm8 cm

15 cm

12 cm

15 cm12 cmFigure A Figure DFigure B Figure C

25 cm

SRX W V

U

T

5x �4x �

(10y � 10)�

B DA

C

EF

50�

B:

Chapter 1 Test, Form 2A11


Ass

essm

ents


1. How many planes can be drawn through any three noncollinear points?A. 0 B. 1 C. 2 D. 3

For Questions 2 and 3, use the figure at the right.

2. Which three points in the figure are collinear?A. A, B, D B. E, C, AC. A, B, C D. F, E, G

3. Name the intersection of the plane P and the plane that contains points B, C, and D.A. point B B. B�D�

C. BC�� D. triangle BCD

4. Find the length of R�S�.

A. 1�156� in. B. 1�

38� in.

C. 1�176� in. D. 1�

58� in.

5. Find the precision for a measurement of 18�12� feet.

A. �12� ft B. �

14� ft C. �

18� ft D. 1 in.

6. Find the length of P�Q�.A. 50.9 cm B. 46.3 cmC. 25.7 cm D. 21.3 cm

7. Find y if B is between A and C, AB is 2y, BC is 6y, and AC is 48.A. 24 B. 8 C. 6 D. 4

8. Find the distance between P(2, 8) and Q(5, 3).A. 9 B. �18� C. �34� D. �170�

9. Find the coordinates of the midpoint of L�B� if L(8, 5) and B(�6, 2).

A. �1, 3�12�� B. �2, 1�

12�� C. �7, 3�

12�� D. �7, 1�

12��

10. Find the coordinates of T given that S is the midpoint of R�T�, R(�4, 2),and S(6, 8).A. (�14, �4) B. (16, 14) C. (2, 10) D. (1, 5)

P R

38.3 cm

12.6 cmQ

1 2in.

R S

PAB

CE

F

D

G

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

NAME DATE PERIOD

SCORE


Chapter 1 Test, Form 2A (continued)11

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.


11. What type of angle is �ABC?A. acute angle B. right angleC. obtuse angle D. straight angle

12. Use a protractor to measure the angles in the figure.Which segment is an angle bisector?A. G�E� B. B�C� C. E�D� D. E�F�


13. Find m�FBD if �FBD and �DBE are complementary and m�FBD is twice m�DBE.A. 30 B. 45C. 60 D. 90

14. Which pair of angles are supplementary?A. �ABE, �CBD B. �ABC, �ABD C. �ABC, �CBD D. �ABC, �EBD

15. Which angle is a vertical angle to �ABE?A. �DBE B. �CBD C. �ABC D. �EBA

16. If m�CBF � 6x � 18, find x so that CB ⊥ BF.A. 90 B. 45 C. 18 D. 12

17. Find m�ABC if m�ABC � 4x � 9 and m�EBD � 7x � 9.A. 6 B. 33 C. 45 D. 73


18. Which describes this figure?A. hexagon, concave, not regularB. pentagon, concave, regularC. hexagon, convex, not regularD. not a polygon

19. What is x for a perimeter of 108 kilometers?A. 53 B. 15 C. 18 D. 105

20. A rectangle has a length of 1.4 feet and a width of 1.2 feet. What is the effecton the perimeter of this rectangle if the length and width are doubled?A. The perimeter is doubled. B. The perimeter is increased by 8.C. The perimeter is multiplied by 4. D. The perimeter is tripled.

Bonus Find m�A if �A is complementary to �B, �B is supplementary to �C, m�B � 15x � 2, and m�C � 25x � 22.

(x � 3) km

F

DE

B

AC

A B

C

DE

F

G

B:

NAME DATE PERIOD

Chapter 1 Test, Form 2B11


Ass

essm

ents


1. Suppose A and B are points. How many lines contain both A and B?A. 0 B. 1C. 2 D. 3


2. Which three points in the figure are collinear?A. C, D, F B. B, C, DC. A, E, F D. A, D, E

3. Name the intersection of the plane that containspoints A, B, and D and the plane P.A. point D B. A�D�

C. triangle BCD D. BD��

4. Find the length of X�Y�.

A. 1�1116� in. B. 1�

58� in.

C. 1�196� in. D. 1�

12� in.

5. Find the precision for a measurement of 34.0 centimeters.A. 0.5 cm B. 1 mm C. 0.5 mm D. 1 cm

6. Find the length of H�J�.A. 11.3 cm B. 12.3 cmC. 13.7 cm D. 45.9 cm

7. Find x if S is between R and T, RS is x � 3, ST is 5x, and RT is 57.A. 9 B. 10 C. 10.8 D. 12

8. Find the distance between M(�2, 3) and N(8, 2).

A. 8 B. �61� C. 10 D. �101�

9. Find the coordinates of the midpoint of A�S� if A(�4, 7) and S(5, 3).

A. (1, 10) B. ��4�12�, 2� C. ��

12�, 5� D. ��

12�, 5�

10. Find the coordinates of T given that S is the midpoint of R�T�, R(2, 6),and S(�2, 0).A. (6, 12) B. (�6, �6) C. (0, 3) D. (�2, 3)

G J

29.1 cm

16.8 cm H

1 2in.

X Y

PCB

D

E

F

A

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

NAME DATE PERIOD

SCORE


Chapter 1 Test, Form 2B (continued)11

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.


11. What type of angle is �BAC?A. acute angle B. right angleC. obtuse angle D. straight angle

12. Use a protractor to measure the angles in the figure.Which segment is an angle bisector?A. A�B� B. C�D� C. C�B� D. A�E�


13. Find m�VSW if �WSR and �VSW are complementaryand m�WSR is four times m�VSW.A. 72 B. 36C. 22.5 D. 18

14. Which pair of angles are supplementary?A. �USV, �VSW B. �VSW, �WSR C. �TSV, �VSW D. �TSR, �USW

15. Which angle is a vertical angle to �UST?A. �VSW B. �USV C. �TSR D. �WSR

16. If m�VSR � 8x � 18, find x so that U�S� ⊥ V�S�.A. 9 B. 12.25 C. 72 D. 90

17. Find m�USW if m�USW � 7x � 34 and m�TSR � 4x � 29.A. 147 B. 113 C. 84 D. 21


18. Which describes this figure?A. hexagon, convex, regularB. pentagon, concave, regularC. pentagon, convex, not regularD. not a polygon

19. What is y for a perimeter of 100 feet?A. 5 B. 15 C. 17 D. 23

20. A square has sides with a length of 5.8 inches. What is the effect on theperimeter of this square if the sides are tripled?A. The perimeter stays the same. B. The perimeter is increased by 12.C. The perimeter is multiplied by 3. D. The perimeter is multiplied by 9.

Bonus Find m�A if �A is supplementary to �B, �B is supplementary to �C, m�B � 12x � 8, and m�C � 8x � 8.

y � 5

y

R

T

U

V W

S

FE

D

CA

B

B:

NAME DATE PERIOD

Chapter 1 Test, Form 2C11


Ass

essm

ents


1. What is another name for line �?

2. Name three points on plane P.

3. Name the intersection of planes P and N.

4. Name three noncoplanar points.

For Questions 5 and 6,use the figure at theright.

5. What is the length ofA�B�?

6. What is the precision of your measurement of A�B�?

7. Find the length of D�E� if D is between points C and E,CD � 6.5 centimeters, and CE � 13.8 centimeters.

8. Find the length of X�Z�.

9. Find x if R�S� � S�T�.

For Questions 10–12, use the coordinate grid.

10. Find the distance between A and B.

11. Find the coordinates of the midpoint of C�D�.

12. Find the coordinates of a point E if Cis the midpoint of A�E�.

13. The vertices of a triangle are located at P(0, 0), Q(8, 6), andR(�3, 4). What is the perimeter of this triangle?

14. Find x and y if U�V� bisects T�W� and UV � 40.

ZT W

U

V

3y � 1

2y � 6

3y � 13x � 2

x

y

O

B

D

A

C

R T

52 in.

6x � 8 S

X Z

4x � 3

2x � 78 cm Y

1cm 2 3 4 5 6

A B

�

P

N

CA B

DE

F

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

NAME DATE PERIOD

SCORE


Chapter 1 Test, Form 2C (continued)11

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

15. Measure �PQR. Then classify �PQRas right, acute, or obtuse.

In the figure, EA�� and EB�� are opposite rays and EC�� bisects �FEG.

16. Find x if m�FEG � 82, and m�FEC � 5x � 11.

17. If m�AED � 16y � 10, find y so that E�D� ⊥ A�B�.


18. Find y.

19. Find m�1.

20. Find m�2.

21. Find x .

For Questions 22–25, use the polygons at the right.

22. Name polygon ABCDEF by its sides. Then classify it asconvex or concave and regular or not regular.

23. Find the perimeter of polygon ABCDEF for x � 4.

24. Find the length of each side of polygon RST.

25. Find the length of one side of a regular pentagon whoseperimeter is the same as the perimeter of RST.

Bonus Find the dimensions of a rectangle whose length is 3 more than twice its width and has a perimeter of 30 centimeters.

6x � 53y � 1

2y � 11

A D

B C R

F E T S

40�

72�1

2

(11x � 24)�

(8y � 16)�

BA

D

GC

F

E

R

P

Q

NAME DATE PERIOD

Chapter 1 Test, Form 2D11


Ass

essm

ents


1. What is another name for line m?

2. Name three points on plane B.

3. Name the intersection of planes A and B.

4. Name three noncollinear points.


5. What is the length of Q�R�?

6. What is the precision of your measurement of Q�R�?

7. Find the length of L�O� if O is between points L and M,LM � 18.6 centimeters, and OM � 12.9 centimeters.

8. Find the length of D�E�.

9. Find y if X�Y� � Y�Z�.


10. Find the distance between Land M.

11. Find the coordinates of the midpoint of M�N�.

12. Find the coordinates of a point Q if P is the midpoint of N�Q�.

13. The vertices of a triangle are located at P(0, 6), Q(8, 12), andR(3, �3). What is the perimeter of this triangle?

14. Find x if R�S� bisects A�B� and RS � 36.

TA B

R

S

18

2y � 6

2y � 525 � 3x

x

y

O

M

NPL

X Z

5y � 11

23 in. Y

D F

24 cm

5x � 133x � 5 E

1 2in.

Q R

A

B

m

T

R

SU

YZ

X

V

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

NAME DATE PERIOD

SCORE


Chapter 1 Test, Form 2D (continued)11

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

15. Measure �ABC. Then classify �ABC as right, acute, or obtuse.

In the figure, RC�� and RD�� are opposite rays and RQ�� bisects �WRV.

16. Find y if m�WRQ � 48 and m�QRV � 7y � 6.

17. Find x so that C�R� ⊥ P�R�.


18. Find x.

19. Find m�1.

20. Find m�2.

21. Find y.

For Questions 22–25, use the polygons at the right.

22. Name polygon RSTUVby its sides. Then classify it as convex orconcave and regular or not regular.

23. Find the perimeter of polygon RSTUV for y � 9.

24. Find the length of each side of polygon ABCD.

25. Find the length of the sides of a regular triangle whoseperimeter is the same as the perimeter of ABCD.

Bonus Find the lengths of the sides of a triangle whose perimeter is 37. The measure of the first side of thetriangle is 8 less than the second side, and the second side is twice the length of the third side.

5y � 8

8x � 3

27 � 4x

S

R T

U D C

A B

V

(9x � 5)� 58�1

2(7y � 27)�

DR

P

C

WQ V

(13x � 12)�

C

A

B

NAME DATE PERIOD

Chapter 1 Test, Form 311


Ass

essm

ents


1. Name five planes shown in the figure.

2. Name a line that is coplanar with AD�� and AB��.

3. Name the intersection of plane P and the plane that containspoints A, B, and E.

For Questions 4 and 5, usethe figure at the right.

4. Find the length of A�B�.

5. Find the precision for the measurement of A�B�.

6. Find two possible lengths for C�D� if C, D, and E are collinear,CE � 15.8 centimeters, and DE � 3.5 centimeters.

7. Find the length of R�S� if S is between R and T, the length of R�S� is �

13� the length of R�T�, RS � 3x � 3, and ST � 2x � 6.

8. Find y if AC � 3y � 5, CB � 4y � 1, AB � 9y � 12, and pointC lies between A and B.

For Questions 9–11, use the coordinate grid at the right.

9. Find the distance between A and B.

10. Find two possible coordinates of a point D on a line containing A�B� so that AD � �

14�AB.

11. Find two values of y for C located at (1, y) and AC � 5.

x

y

O

B

A

6 7in.

A B

P

A

E

F

D

C

B

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

NAME DATE PERIOD

SCORE


Chapter 1 Test, Form 3 (continued)11

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

12. Find y if S is the midpoint of R�T�, T is the midpoint of R�U�,RS � 6x � 5, ST � 8x � 1, and TU � 11y � 13.

13. Find all values of x that will make �A an obtuse angle givenm�A � 12x � 6.

14. Find m�RST if ST�� bisects �RSU and SU�� bisects �TSV.

15. Find m�1 if �1 is complementary to �2, �2 is supplementaryto �3, and m�3 � 126.

16. Find y if XW�� ⊥ XZ��, Y is in the interior of �WXZ,m�WXY � 6y � 3, and m�YXZ � 4y � 13.

17. Find the length of L�M� if ON�� is the bisector of L�M� and LN � 3x � 2.

For Questions 18 and 19, use the coordinate grid.

18. Graph polygon ABCD with vertices A(4, 3), B(0, 3), C(�2, 2),and D(�5, 6). Then name polygon ABCD by its number ofsides and classify it as convex or concave and regular orirregular.

19. Find the perimeter of polygon ABCD.

20. Find the perimeter of regular triangle DEF if DE � 28 � 3yand EF � 2y � 3.

Bonus Suppose a regular quadrilateral and a regular triangle havethe same perimeter. The sides of the triangle are 3 incheslonger than the sides of the quadrilateral. Find the lengthsof the sides of the quadrilateral and the triangle.

N ML

O

7x � 1

V

U

T

R

S

(x � 2y � 1)�

(6x � 9)�

(2y � 5)�

NAME DATE PERIOD

Chapter 1 Open-Ended Assessment11


Ass

essm

ents

Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solution in more than one way orinvestigate beyond the requirements of the problem.

1. Draw and label a figure that shows that plane R contains both lines s andAC�� that intersect at point B. Name three collinear points in plane R.

2. Draw a line on a coordinate plane so that you can determine at least twopoints on the graph. Label those two points D and G.

a. Find the distance between points D and G.

b. Find the coordinates of E, the midpoint of D�G�.

c. Find the coordinates of point H given that G is the midpoint of D�H�.

3. Rectangle WXYZ has a length that is 5 more than three times its width.

a. Draw and label a figure for rectangle WXYZ.

b. Write an algebraic expression for the perimeter of the rectangle.

c. Find the width if the perimeter is 58 millimeters. Explain how you cancheck that your answer is correct.

d. Use a ruler to draw and label P�Q�, which is congruent to the segmentrepresenting the length of rectangle WXYZ. What is the measure of P�Q�?

e. Explain how to find the precision of the measurement of P�Q�.

4. Draw an acute angle, �ABC. Let m�ABC � 6x � 1.

a. Use a protractor to determine the measure of �ABC. Use thismeasure to determine the value of x.

b. Explain how you would determine the measure of an angle that iscomplementary to �ABC.

c. Explain how you would determine the measure of an angle that issupplementary to �ABC.

5. RS�� is in the interior of �TRU, m�TRS � 4x � 6, and m�SRU � 8x � 6.

a. Draw �TRU and RS��.

b. Determine the value of x that will make RS�� an angle bisector. Explainyour steps.

c. Describe the relationship between RU�� and RT�� when x � 7.5.

NAME DATE PERIOD

SCORE


Chapter 1 Vocabulary Test/Review11

Choose from the terms above to complete each sentence.

1. Two lines are if they intersect to form a right angle.

2. Two angles are if their measures have a sum of 90°.

3. When two rays intersect with a common endpoint a(n) is formed.

4. The is the point located halfway between theendpoints of a segment.

5. are nonadjacent angles formed by the intersection oftwo lines.

6. A(n) divides an angle into two congruent angles.

7. Two angles are if their measures have a sum of 180°.

8. Two angles that lie in the same plane are called ifthey share a common side and a common vertex.

9. A(n) is an angle whose measure is less than 90°.

10. Two segments are if they have the same measure.

In your own words—

11. Explain how to find the precision of a measurement of 5�

12� inches on a ruler marked in half inches.

12. Describe what is meant by betweenness of points usingcollinear points M, P, and Q.

?

?

?

?

?

?

?

?

?

? 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

acute angleadjacent anglesangleangle bisectorbetweenness collinearcomplementary concavecongruentconstruction

convexcoplanardegreedistanceexteriorinteriorlineline segmentlinear pairmidpoint

n-gonobtuse angleopposite raysperimeterperpendicularplanepointpolygonprecisionray

regular polygonrelative errorright anglesegment bisectorsidesspacesupplementaryundefined termsvertexvertical angles

NAME DATE PERIOD

SCORE

Chapter 1 Quiz (Lessons 1–1 and 1–2)

11


Ass

essm

ents

NAME DATE PERIOD

SCORE

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


1. What is another name for line �?

2. Name the intersection of lines � and m.



4. Find the length of A�B�.

5. Find the precision of the measurement of A�B�.

6. Find the length of U�W� if W is between U and V,UV � 16.8 centimeters, and VW � 7.9 centimeters.

7. Find x if RS � 24 centimeters.

8. Find the length of L�O� if M is between L and O, LM � 7x � 9,MO � 14 inches, and LO � 10x � 7.

9. Find x if P�Q� � R�S�, PQ � 9x � 7, and RS � 29.

10. STANDARDIZED TEST PRACTICE Which of the following isnot an undefined term in geometry?A. plane B. point C. bisector D. line

R S

10 cm6x � 4

T

1in.

A B

R T

SU

m

�V

Chapter 1 Quiz (Lesson 1–3)

11

1.

2.

3.

4.

5.

1. Find the coordinates of the midpoint of A�B� for A(2, 5) and B(6, 9).

2. Find the coordinates of D if E is the midpoint of C�D�, for C(�3, 4) and E(0, 1).

3. What is the length of F�H� if G is the midpoint, FG � 12x � 5,and GH � 7x?

4. What is the length of U�V� if WX�� is the segment bisector of U�V� at point Z?

5. STANDARDIZED TEST PRACTICE Find the distance betweenA(�2, 1) and B(4, �3).A. 52 B. �52� C. �20� D. �8�

U

V9x � 2

6x � 8

ZX

W

NAME DATE PERIOD

SCORE


Chapter 1 Quiz (Lessons 1–4 and 1–5)

11

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


1. Name the vertex of �1.

2. Classify �TSV as right, acute, or obtuse.

3. Name a point in the exterior of �RTS.

4. Find m�TSU if S�U� bisects �TSV,m�TSU � 4y � 11, and m�USV � 6y � 5.

5. Name a pair of adjacent angles.

6. Name a pair of vertical angles.

7. Find m�DBC if m�ABC � 5x � 3 and �ABD � �DBC.

For Questions 8 and 9, lines p and q intersect to formadjacent angles 1 and 2.

8. If m�1 � 7x � 6 and m�2 � 8x � 6, find x so that p isperpendicular to q.

9. If m�1 � 4x � 3 and m�2 � 3x � 8, find x so that �1 issupplementary to �2.

10. STANDARDIZED TEST PRACTICE The difference betweentwo complementary angles is 14. Which is the measure of oneof those angles?A. 14 B. 52 C. 83 D. 90

(3x � 2)�B

A

DC

ST

U V

W

PR

1

NAME DATE PERIOD

SCORE

Chapter 1 Quiz (Lesson 1–6)

11

1.

2.

3.

4.

5.

1. Draw a concave pentagon.

2. Find the length of each side of a regular hexagon whoseperimeter is 84 meters.

3. If x � 5, find the perimeter of the rectangle whose length is 6x � 4 and whose width is 3x � 2.

4. The perimeter of a convex pentagon is 15 feet. What is theeffect on its perimeter if each side is doubled?

5. For what value of y is triangle ABC a regular triangle?

7y � 12

5y � 209y � 4

B

CA

NAME DATE PERIOD

SCORE

Chapter 1 Mid-Chapter Test (Lessons 1–1 through 1–3)

11


Ass

essm

ents


1. Which point is coplanar with points A and C?A. A B. BC. C D. D

2. Name the point of intersection of plane M and DE��.A. D B. E C. B D. M


3. What is the length of A�B�?

A. about 1�14� in. B. about 1�

12� in.

C. about 1�34� in. D. about 2 in.

4. What is the precision for the measurement of A�B�?

A. 1 in. B. �12� in. C. �

14� in. D. �

18� in.

5. What is the length of T�S�?A. 9.4 cm B. 8.9 cmC. 4.7 cm D. 4.2 cm

R S

8.9 cm

4.7 cm T

1 2in.

A B

MBCA

D

E

6.

7.

8.

9.

10.

NAME DATE PERIOD

SCORE

1.

2.

3.

4.

5.

Part II


6. Find the distance between R and S.

7. Find the coordinates of the midpoint of T�U�.

8. Find the coordinates of a point M given that U is the midpoint of M�S�.

9. Find y if M is the midpoint of L�N�.

10. In the figure, WZ�� bisects X�Y�. Find the length of X�Y�.

X

Y6x � 11

4x � 5V

Z

W

L N

6y � 59y � 4

M

x

y

O

R US

T

Part I Write the letter for the correct answer in the blank at the right of each question.


Chapter 1 Cumulative Review(Chapter 1)

11

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.


1. Name three points that are collinear.(Lesson 1-1)

2. Name the intersection of AE�� and CG��.(Lesson 1-1)

Find the measurement of each segment. Assume that theart is not drawn to scale. (Lesson 1-2)

3. A�B�

4. K�N�

5. Use the Pythagorean Theorem to find the distance betweenA(�12, 13) and B(�2, �11). (Lesson 1-3)

6. Find the coordinates of B if A has coordinates (3, 5) and Y(�2, 3) is the midpoint of A�B�. (Lesson 1-3)

For Questions 7 and 8, use the figure to name the vertex and sides of each angle. Then measure and classify each angle. (Lesson 1-4)

7. �JNK 8. �HNK

For Questions 9–11, use the figure at the right. (Lesson 1-5)

9. Name a pair of supplementarynonadjacent angles.


11. Name an angle complementary to �CFD.

12. If m�HJK � 7y � 2 and m�PQR � 133, find y so that �HJKis supplementary to �PQR. (Lesson 1-5)

13. Name this polygon by its number of sides and then classify it as convex or concave and regularor irregular. (Lesson 1-6)

14. Find the perimeter of �ABC if A(1, 1), B(4, �3), and C(�3, �2).(Lesson 1-6)

15. Find the length of each side of a regular pentagon whoseperimeter is 90 centimeters. (Lesson 1-6)

A F DE

B C

G60� 30�

120�

N

K

M

J

H

L

157�

77�26�

J K L M N

4 mm 3 mm

A C5 cm

2 cmB

A

C

E

B

D

FG

H

NAME DATE PERIOD

SCORE

Standardized Test Practice (Chapter 1)


1. Which object models a line? (Lesson 1-1)

A. a fly B. a wall C. a meter stick D. a diskette

2. Which figure shows AB�� and point G contained in plane R ? (Lesson 1-1)

E. F.

G. H.

3. What is the precision of a measurement of 49.5 centimeters on aruler with millimeter marks? (Lesson 1-2)

A. 49 cm to 50 cm B. 49.0 cm to 50.0 cmC. 490 mm to 500 mm D. 494.5 mm to 495.5 mm

4. When segments have the same measure, they are said to be. (Lesson 1-2)

E. accurate F. congruentG. precise H. constructed

5. Find the distance between A(�3, 5) and B(4, 2), to the nearesthundredth. (Lesson 1-3)

A. 6.75 B. 7.62 C. 8.06 D. 10

6. Find EF if E is the midpoint of D�F�, DE � 15 � 3x, and EF � x � 3. (Lesson 1-3)

E. 1 F. 3 G. 6 H. 9

For Questions 7–9, use the figure.

7. What is another name for �2? (Lesson 1-4)

A. �WYX B. �WXYC. �3 D. �Y

8. Which angles form a linear pair? (Lesson 1-5)

E. �1 and �3 F. �2 and �5 G. �2 and �3 H. �1 and �4

9. Name the angle that is vertical to �3. (Lesson 1-5)

A. �1 B. �2 C. �3 D. �4

10. Find the length of one side of a regular hexagon whose perimeteris 75 feet. (Lesson 1-6)

E. 25 ft F. 18.75 ft G. 15 ft H. 12.5 ft

WY

X14

235

?

A

B

G RA B

G

R

A BR

GA BG R

NAME DATE PERIOD

SCORE

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. E F G H

A B C D

E F G H

A B C D

E F G H

A B C D

E F G H

A B C D

E F G H

A B C D

Ass

essm

ents

11


Standardized Test Practice (continued)

11. How many points name a line? (Lesson 1-1)

12. What is the measure of A�C�? (Lesson 1-2)

For Questions 13–15, HL�� bisects �KHI andHG�� and HI�� are opposite rays.

13. If �1 � �2, m�KHG � 70, and m�1 � 3d � 2,find d. (Lesson 1-4)

14. If m�2 � a � 15 and m�3 � a � 35, find a sothat HL�� ⊥ HJ��. (Lesson 1-5)

15. Find m�4, if m�GHL � 125. (Lesson 1-5)

G H I

J

KL

1 42 3

A B C3.7 5.2

NAME DATE PERIOD

Part 2: Grid In

Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.

Part 3: Short Response

Instructions: Show your work or explain in words how you found your answer.

11. 12.

13. 14.

15.

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

16. Find the length of X�Z� if Y(�4, 4) is the midpoint of X�Z� and X has coordinates (2, �4). (Lesson 1-3)

17. Find the perimeter of this hexagon.(Lesson 1-6)

18. Find the measure of W�X�, if the perimeter of pentagon UVWXY is 48 units. (Lesson 1-6)

10 � a

2aW X

U

V Y

4a � 7

30 m

20 m

7 m 6 m

10 m8.5 m

16.

17.

18.

2 8 . 9

1 1

5 5

2 0

11

Standardized Test PracticeStudent Record Sheet (Use with pages 58–59 of the Student Edition.)

11

© Glencoe/McGraw-Hill A1 Glencoe Geometry

An

swer

s

Select the best answer from the choices given and fill in the corresponding oval.

1 4 7

2 5 8

3 6 9 DCBADCBADCBA

DCBADCBADCBA

DCBADCBADCBA

NAME DATE PERIOD

Part 1 Multiple ChoicePart 1 Multiple Choice

Part 2 Short Response/Grid InPart 2 Short Response/Grid In

Part 3 Open-EndedPart 3 Open-Ended

Solve the problem and write your answer in the blank.

For Questions 14 and 15, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.

10 14 15

11

12

13

14 (grid in)

15 (grid in)

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

Record your answers for Questions 16–17 on the back of this paper.


Stu

dy G

uid

e a

nd I

nte

rven

tion

Po

ints

,Lin

es,a

nd

Pla

nes

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-1

1-1

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Geo

met

ry

Lesson 1-1

Nam

e Po

ints

, Lin

es, a

nd

Pla

nes

In g

eom

etry

,a p

oin

tis

a l

ocat

ion

,a l

ine

con

tain

spo

ints

,an

d a

pla

ne

is a

fla

t su

rfac

e th

at c

onta

ins

poin

ts a

nd

lin

es.I

f po

ints

are

on

th

e sa

me

lin

e,th

ey a

re c

olli

nea

r.If

poi

nts

on

are

th

e sa

me

plan

e,th

ey a

re c

opla

nar

.

Use

th

e fi

gure

to

nam

e ea

ch o

f th

e fo

llow

ing.

a.a

lin

e co

nta

inin

g p

oin

t A

Th

e li

ne

can

be

nam

ed a

s �.

Als

o,an

y tw

o of

th

e th

ree

poin

ts o

n t

he

lin

e ca

n b

e u

sed

to n

ame

it.

AB

�� ,

AC

�� ,

or B

C��

�

b.

a p

lan

e co

nta

inin

g p

oin

t D

Th

e pl

ane

can

be

nam

ed a

s pl

ane

Nor

can

be

nam

ed u

sin

g th

ree

non

coll

inea

r po

ints

in

th

e pl

ane,

such

as

plan

e A

BD

,pla

ne

AC

D,a

nd

so o

n.

Ref

er t

o th

e fi

gure

.

1.N

ame

a li

ne

that

con

tain

s po

int

A.

AB

�� ,

AC

�� ,

BC

�� ,

or

�

2.W

hat

is

anot

her

nam

e fo

r li

ne

m?

BD

��

3.N

ame

a po

int

not

on

AC

�� .

Do

r E

4.N

ame

the

inte

rsec

tion

of

AC

��

and

DB

�� .

B

5.N

ame

a po

int

not

on

lin

e �

or l

ine

m.E

Dra

w a

nd

lab

el a

pla

ne

Qfo

r ea

ch r

elat

ion

ship

.

6.A

B��

�is

in

pla

ne

Q.

7.S

T��

�in

ters

ects

AB

��

at P

.

8.P

oin

t X

is c

olli

nea

r w

ith

poi

nts

Aan

d P

.A

nsw

ers

for

Exe

rcis

es 6

–10

9.P

oin

t Y

is n

ot c

olli

nea

r w

ith

poi

nts

Tan

d P

.

10.L

ine

�co

nta

ins

poin

ts X

and

Y.

�Q

AB

S P

TY

X

�

PmA

B EC

D

�

N

AB

C

DEx

ampl

eEx

ampl

e

Exer

cises

Exer

cises

©G

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Geo

met

ry

Poin

ts, L

ines

, an

d P

lan

es in

Sp

ace

Sp

ace

is a

bou

ndl

ess,

thre

e-di

men

sion

al s

et o

fal

l po

ints

.It

con

tain

s li

nes

an

d pl

anes

.

a.H

ow m

any

pla

nes

ap

pea

r in

th

e fi

gure

?

Th

ere

are

thre

e pl

anes

:pla

ne

N,p

lan

e O

,an

d pl

ane

P.

b.

Are

poi

nts

A,B

,an

d D

cop

lan

ar?

Yes.

Th

ey a

re c

onta

ined

in

pla

ne

O.

Ref

er t

o th

e fi

gure

.

1.N

ame

a li

ne

that

is

not

con

tain

ed i

n p

lan

e N

.A

B��

�

2.N

ame

a pl

ane

that

con

tain

s po

int

B.

pla

ne

N,p

lan

e A

BC

,pla

ne

AB

D,p

lan

e E

BC

,p

lan

e E

BD

3.N

ame

thre

e co

llin

ear

poin

ts.

A,B

,E

Ref

er t

o th

e fi

gure

.

4.H

ow m

any

plan

es a

re s

how

n i

n t

he

figu

re?

6

5.A

re p

oin

ts B

,E,G

,an

d H

copl

anar

? E

xpla

in.

No

;B

,G,a

nd

Hlie

in p

lan

e B

GH

,bu

t E

do

es n

ot.

6.N

ame

a po

int

copl

anar

wit

h D

,C,a

nd

E.

Fo

r J

Dra

w a

nd

lab

el a

fig

ure

for

eac

h r

elat

ion

ship

.

7.P

lan

es M

andN

inte

rsec

t in

HJ

�� .

8.L

ine

ris

in

pla

ne

N,l

ine

sis

in

pla

ne

M,a

nd

lin

es r

and

sin

ters

ect

at p

oin

t J

.

9.L

ine

tco

nta

ins

poin

t H

and

lin

e td

oes

not

lie

in

pla

ne

Mor

plan

e N

.A

nsw

ers

for

Exe

rcis

es 7

–9

N

Ms

t

r

HJ

AB C

D

EFG

HI

J

N

A

C

B

D

E

NO

P

AB

CD

Stu

dy G

uid

e a

nd I

nte

rven

tion

(con

tinued

)

Po

ints

,Lin

es,a

nd

Pla

nes

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-1

1-1

Exam

ple

Exam

ple

Exer

cises

Exer

cises

Answers (Lesson 1-1)


An

swer

s

Skil

ls P

ract

ice

Po

ints

,Lin

es,a

nd

Pla

nes

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-1

1-1

©G

lenc

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Geo

met

ry

Lesson 1-1

Ref

er t

o th

e fi

gure

.

1.N

ame

a li

ne

that

con

tain

s po

int

D.

po

r C

D��

�

2.N

ame

a po

int

con

tain

ed i

n l

ine

n.A

or

B

3.W

hat

is

anot

her

nam

e fo

r li

ne

p?C

D��

�o

r D

C��

�

4.N

ame

the

plan

e co

nta

inin

g li

nes

nan

d p.

Sam

ple

an

swer

:p

lan

e G

Dra

w a

nd

lab

el a

fig

ure

for

eac

h r

elat

ion

ship

.S

amp

le a

nsw

ers

are

giv

en.

5.P

oin

t K

lies

on

RT

�� .

6.P

lan

e J

con

tain

s li

ne

s.

7.Y

P� �

�li

es i

n p

lan

e B

and

con

tain

s 8.

Lin

es q

and

fin

ters

ect

at p

oin

t Z

poin

t C

,bu

t do

es n

ot c

onta

in p

oin

t H

.in

pla

ne

U.

Ref

er t

o th

e fi

gure

.

9.H

ow m

any

plan

es a

re s

how

n i

n t

he

figu

re?

5

10.H

ow m

any

of t

he

plan

es c

onta

in p

oin

ts F

and

E?

2

11.N

ame

fou

r po

ints

th

at a

re c

opla

nar

.

A,B

,E,F

or

B,C

,D,E

or

A,C

,D,F

12.A

re p

oin

ts A

,B,a

nd

Cco

plan

ar?

Exp

lain

.

Yes;

po

ints

A,B

,an

d C

lie in

pla

ne

W.

WA

BE

CDF

U

qf

Z

HP

B

CY

J

sT

RK

Gn

AB

D

C

p

©G

lenc

oe/M

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ncoe

Geo

met

ry

Ref

er t

o th

e fi

gure

.

1.N

ame

a li

ne

that

con

tain

s po

ints

Tan

d P

.

g,T

P��

� ,T

N��

� ,N

P��

�

2.N

ame

a li

ne

that

in

ters

ects

th

e pl

ane

con

tain

ing

poin

ts Q

,N,a

nd

P.

jor

MT

��

3.N

ame

the

plan

e th

at c

onta

ins

TN

��

and

QR

�� .

Sam

ple

an

swer

:p

lan

e S

Dra

w a

nd

lab

el a

fig

ure

for

eac

h r

elat

ion

ship

.S

amp

le a

nsw

ers

are

giv

en.

4.A

K��

�an

d C

G��

�in

ters

ect

at p

oin

t M

5.A

line

con

tain

s L

(�4,

�4)

and

M(2

,3).

Lin

e in

pla

ne

T.q

is i

n t

he

sam

e co

ordi

nat

e pl

ane

but

does

not

in

ters

ect

LM

� �� .

Lin

e q

con

tain

s po

int

N.

Ref

er t

o th

e fi

gure

.

6.H

ow m

any

plan

es a

re s

how

n i

n t

he

figu

re?

6

7.N

ame

thre

e co

llin

ear

poin

ts.

S,X

,M

8.A

re p

oin

ts N

,R,S

,an

d W

copl

anar

? E

xpla

in.

No

;sa

mp

le a

nsw

er:

po

ints

N,R

,an

d S

lie

in p

lan

e A

,bu

t p

oin

t W

do

es n

ot.

VIS

UA

LIZA

TIO

NN

ame

the

geom

etri

c te

rm(s

) m

odel

ed b

y ea

ch o

bje

ct.

9.10

.11

.

pla

ne

and

lin

ep

oin

tlin

es

12.a

car

an

ten

na

13.a

lib

rary

car

dlin

e an

d p

oin

tp

lan

e

strin

gs

tip o

f pin

STOP

AM

N

PW

S XRQ

T

L

M

N

q

x

y

O

KT

M

C

GA

S

j

ghTM

NQ

R

P

Pra

ctic

e (

Ave

rag

e)

Po

ints

,Lin

es,a

nd

Pla

nes

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

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1-1

1-1



Readin

g t

o L

earn

Math

em

ati

csP

oin

ts,L

ines

,an

d P

lan

es

NA

ME

____

____

____

____

____

____

____

____

____

____

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AT

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1-1

1-1

©G

lenc

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w-H

ill5

Gle

ncoe

Geo

met

ry

Lesson 1-1

Pre-

Act

ivit

yW

hy

do

chai

rs s

omet

imes

wob

ble

?

Rea

d th

e in

trod

uct

ion

to

Les

son

1-1

at

the

top

of p

age

6 in

you

r te

xtbo

ok.

•F

ind

thre

e pe

nci

ls o

f di

ffer

ent

len

gth

s an

d h

old

them

upr

igh

t on

you

rde

sk s

o th

at t

he

thre

e pe

nci

l po

ints

do

not

lie

alo

ng

a si

ngl

e li

ne.

Can

you

plac

e a

flat

sh

eet

of p

aper

or

card

boar

d so

th

at i

t to

uch

es a

ll t

hre

e pe

nci

lpo

ints

?ye

s•

How

man

y w

ays

can

you

do

this

if

you

kee

p th

e pe

nci

l po

ints

in

th

e sa

me

posi

tion

?o

ne

•H

ow w

ill

you

r an

swer

ch

ange

if

ther

e ar

e fo

ur

pen

cil

poin

ts?

Sam

ple

answ

er:

It m

ay n

ot

be

po

ssib

le t

o p

lace

th

e p

aper

to

to

uch

all f

ou

r p

oin

ts.

Rea

din

g t

he

Less

on

1.C

ompl

ete

each

sen

ten

ce.

a.P

oin

ts t

hat

lie

on

th

e sa

me

lie

are

call

ed

poin

ts.

b.

Poi

nts

th

at d

o n

ot l

ie i

n t

he

sam

e pl

ane

are

call

ed

poin

ts.

c.T

her

e is

exa

ctly

on

e th

rou

gh a

ny

two

poin

ts.

d.

Th

ere

is e

xact

ly o

ne

thro

ugh

an

y th

ree

non

coll

inea

r po

ints

.

2.R

efer

to

the

figu

re a

t th

e ri

ght.

Indi

cate

wh

eth

er e

ach

st

atem

ent

is t

rue

or f

alse

.

a.P

oin

ts A

,B,a

nd

Car

e co

llin

ear.

fals

e

b.

Th

e in

ters

ecti

on o

f pl

ane

AB

Can

d li

ne

mis

poi

nt

P.

tru

e

c.L

ine

�an

d li

ne

mdo

not

in

ters

ect.

fals

e

d.

Poi

nts

A,P

,an

d B

can

be

use

d to

nam

e pl

ane

U.

fals

e

e.L

ine

�li

es i

n p

lan

e A

CB

.tr

ue

3.C

ompl

ete

the

figu

re a

t th

e ri

ght

to s

how

th

e fo

llow

ing

rela

tion

ship

:Lin

es �

,m,a

nd

nar

e co

plan

ar a

nd

lie

in

plan

e Q

.Lin

es �

and

min

ters

ect

at p

oin

t P

.Lin

e n

inte

rsec

ts l

ine

mat

R,b

ut

does

not

in

ters

ect

lin

e �.

Hel

pin

g Y

ou

Rem

emb

er

4.R

ecal

l or

loo

k in

a d

icti

onar

y to

fin

d th

e m

ean

ing

of t

he

pref

ix c

o-.W

hat

doe

s th

is p

refi

xm

ean

? H

ow c

an i

t h

elp

you

rem

embe

r th

e m

ean

ing

of c

olli

nea

r?S

amp

le a

nsw

er:T

he

pre

fix

co-

mea

ns

tog

eth

er.T

he

wo

rd c

olli

nea

rco

nta

ins

the

wo

rd li

ne,

so c

olli

nea

rm

ean

s to

get

her

on

a li

ne.

Qn

m

�P

R

U

m

�P

C

D

B

A

pla

ne

line

no

nco

pla

nar

colli

nea

r

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lenc

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w-H

ill6

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ncoe

Geo

met

ry

Po

ints

an

d L

ines

on

a M

atri

xA

mat

rix

is a

rec

tan

gula

r ar

ray

of r

ows

and

colu

mn

s.P

oin

ts a

nd

lin

es o

n a

mat

rix

are

not

def

ined

in

th

e sa

me

way

as

in E

ucl

idea

nge

omet

ry.A

poi

nt

on a

mat

rix

is a

dot

,wh

ich

can

be

smal

l or

larg

e.A

lin

e on

a m

atri

x is

a p

ath

of

dots

th

at “

lin

e u

p.”

Bet

wee

ntw

o po

ints

on

a l

ine

ther

e m

ay o

r m

ay n

ot b

e ot

her

poi

nts

.Th

ree

exam

ples

of

lin

es a

re s

how

n a

t th

e u

pper

rig

ht.

Th

e br

oad

lin

e ca

nbe

th

ough

t of

as

a si

ngl

e li

ne

or a

s tw

o n

arro

w l

ines

sid

e by

sid

e.

Dot

-mat

rix

prin

ters

for

com

pute

rs u

sed

dots

to

form

ch

arac

ters

.T

he

dots

are

oft

en c

alle

d p

ixel

s.T

he

mat

rix

at t

he

righ

t sh

ows

how

a d

ot-m

atri

x pr

inte

r m

igh

t pr

int

the

lett

er P

.

An

swer

s m

ay v

ary.

Sam

ple

an

swer

s ar

e sh

ow

n.

Dra

w p

oin

ts o

n e

ach

mat

rix

to c

reat

e th

e gi

ven

fig

ure

s.

1.D

raw

tw

o in

ters

ecti

ng

lin

es t

hat

hav

e2.

Dra

w t

wo

lin

es t

hat

cro

ss b

ut

hav

e fo

ur

poin

ts i

n c

omm

on.

no

com

mon

poi

nts

.

3.M

ake

the

nu

mbe

r 0

(zer

o) s

o th

at i

t4.

Mak

e th

e ca

pita

l le

tter

O s

o th

at i

tex

ten

ds t

o th

e to

p an

d bo

ttom

sid

esex

ten

ds t

o ea

ch s

ide

of t

he

mat

rix.

of t

he

mat

rix.

5.U

sin

g se

para

te g

rid

pape

r,m

ake

dot

desi

gns

for

seve

ral

oth

er l

ette

rs.W

hic

h w

ere

the

easi

est

and

wh

ich

wer

e th

e m

ost

diff

icu

lt?

See

stu

den

ts’w

ork

.

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

E__

____

____

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ER

IOD

____

_

1-1

1-1



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

Lin

ear

Mea

sure

an

d P

reci

sio

n

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

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_

1-2

1-2

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lenc

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ill7

Gle

ncoe

Geo

met

ry

Lesson 1-2

Mea

sure

Lin

e Se

gm

ents

A p

art

of a

lin

e be

twee

n t

wo

endp

oin

ts i

s ca

lled

a l

ine

segm

ent.

Th

e le

ngt

hs

of M �

N�an

d R�

S�ar

e w

ritt

en a

s M

Nan

d R

S.W

hen

you

mea

sure

ase

gmen

t,th

e pr

ecis

ion

of

the

mea

sure

men

t is

hal

f of

th

e sm

alle

st u

nit

on

th

e ru

ler.

Fin

d t

he

len

gth

of

M�N�

.

Th

e lo

ng

mar

ks a

re c

enti

met

ers,

and

the

shor

ter

mar

ks a

re m

illi

met

ers.

Th

e le

ngt

h o

f M �

N�is

3.4

cen

tim

eter

s.T

he

mea

sure

men

t is

ac

cura

te t

o w

ith

in 0

.5 m

illi

met

er,s

o M �

N�is

betw

een

3.3

5 ce

nti

met

ers

and

3.45

cen

tim

eter

s lo

ng.

1cm

23

4

MN

Fin

d t

he

len

gth

of

R�S�

.

Th

e lo

ng

mar

ks a

re i

nch

es a

nd

the

shor

t m

arks

are

qu

arte

r in

ches

.Th

e le

ngt

h o

f R �

S�is

abo

ut

1�3 4�

inch

es.T

he

mea

sure

men

t is

accu

rate

to

wit

hin

one

half

of

a qu

arte

r in

ch,

or �1 8�

inch

,so

R�S�

is b

etw

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1�5 8�

inch

es a

nd

1�7 8�

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es l

ong.1

2in

.

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ple1

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cises

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cises

Fin

d t

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lin

e se

gmen

t or

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ject

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5 cm

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.

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m

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Geo

met

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Cal

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easu

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On

PQ

�� ,

to s

ay t

hat

poi

nt

Mis

be

twee

n p

oin

ts P

and

Qm

ean

s P,

Q,a

nd

Mar

e co

llin

ear

and

PM

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Q�

PQ

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On

AC

�� ,

AB

�B

C�

3 cm

.We

can

say

th

at t

he

segm

ents

are

con

gru

ent,

or A �

B��

B�C�

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shes

on

th

e fi

gure

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dica

te w

hic

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gmen

ts a

re c

ongr

uen

t.

AB

C

QM

P

Stu

dy G

uid

e a

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nte

rven

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(con

tinued

)

Lin

ear

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sure

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n

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ME

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enti

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um

e th

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gure

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erm

ine

wh

eth

er e

ach

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men

ts i

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ier

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Use

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ach

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,4),

P(6

,3)

21.Q

(3,9

),P

(�1,

5)

Q(8

,4)

Q(7

,2)

N(�

5,1)

–6–4

–20

24

68

1012

AB

CD

E

x

y

O

D

S

x

y

O

F

G

–6–4

–20

24

68

10

JK

LM

N

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lenc

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Gle

ncoe

Geo

met

ry

Use

th

e n

um

ber

lin

e to

fin

d e

ach

mea

sure

.

1.V

W4

2.T

V5

3.S

T3

4.S

V8

Use

th

e P

yth

agor

ean

Th

eore

m t

o fi

nd

th

e d

ista

nce

bet

wee

n e

ach

pai

r of

poi

nts

.

5.6.

�65�

�8.

1�

113

��

10.6

Use

th

e D

ista

nce

For

mu

la t

o fi

nd

th

e d

ista

nce

bet

wee

n e

ach

pai

r of

poi

nts

.

7.L

(�7,

0),Y

(5,9

)8.

U(1

,3),

B(4

,6)

15�

18��

4.2

Use

th

e n

um

ber

lin

e to

fin

d t

he

coor

din

ate

of t

he

mid

poi

nt

of e

ach

seg

men

t.

9.R �

T�1

10.Q�

R��

4

11.S�

T�2�

1 2�12

.P�R�

�5

�1 2�

Fin

d t

he

coor

din

ates

of

the

mid

poi

nt

of a

seg

men

t h

avin

g th

e gi

ven

en

dp

oin

ts.

13.K

(�9,

3),H

(5,7

)14

.W(�

12,�

7),T

(�8,

�4)

(�2,

5)(�

10,�

5.5)

Fin

d t

he

coor

din

ates

of

the

mis

sin

g en

dp

oin

t gi

ven

th

at E

is t

he

mid

poi

nt

of D�

F�.

15.F

(5,8

),E

(4,3

)16

.F(2

,9),

E(�

1,6)

17.D

(�3,

�8)

,E(1

,�2)

D(3

,�2)

D(�

4,3)

F(5

,4)

18.P

ERIM

ETER

Th

e co

ordi

nat

es o

f th

e ve

rtic

es o

f a

quad

rila

tera

l ar

e R

(�1,

3),S

(3,3

),T

(5,�

1),a

nd

U(�

2,�

1).F

ind

the

peri

met

er o

f th

e qu

adri

late

ral.

Rou

nd

to t

he

nea

rest

ten

th.

19.6

un

its

–6–4

–10

–8–2

02

46

PQ

RS

T

x

y

O

E

S

x

y

OM

Z

–6–4

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46

8

ST

UV

W

Pra

ctic

e (

Ave

rag

e)

Dis

tan

ce a

nd

Mid

po

ints

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

____

_

1-3

1-3



Readin

g t

o L

earn

Math

em

ati

csD

ista

nce

an

d M

idp

oin

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

E__

____

____

__P

ER

IOD

____

_

1-3

1-3

©G

lenc

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w-H

ill17

Gle

ncoe

Geo

met

ry

Lesson 1-3

Pre-

Act

ivit

yH

ow c

an y

ou f

ind

th

e d

ista

nce

bet

wee

n t

wo

poi

nts

wit

hou

t a

rule

r?

Rea

d th

e in

trod

uct

ion

to

Les

son

1-3

at

the

top

of p

age

21 i

n y

our

text

book

.

•L

ook

at t

he

tria

ngl

e in

th

e in

trod

uct

ion

to

this

les

son

.Wh

at i

s th

e sp

ecia

ln

ame

for

A�B�

in t

his

tri

angl

e?hy

po

ten

use

•F

ind

AB

in t

his

fig

ure

.Wri

te y

our

answ

er b

oth

as

a ra

dica

l an

d as

ade

cim

al n

um

ber

rou

nde

d to

th

e n

eare

st t

enth

.�

61�u

nit

s;7.

8 u

nit

s

Rea

din

g t

he

Less

on

1.M

atch

eac

h f

orm

ula

or

expr

essi

on i

n t

he

firs

t co

lum

n w

ith

on

e of

th

e n

ames

in

th

ese

con

d co

lum

n.

a.d

��

(x2

��

x 1)2

��

(y2

��

y 1)2

�ii

i.P

yth

agor

ean

Th

eore

m

b.

�a� 2

b�

vii

.Dis

tan

ce F

orm

ula

in

th

e C

oord

inat

e P

lan

e

c.X

Y�

| a�

b| i

vii

i.M

idpo

int

of a

Seg

men

t in

th

e C

oord

inat

e P

lan

e

d.

c2�

a2�

b2i

iv.

Dis

tan

ce F

orm

ula

on

a N

um

ber

Lin

e

e.��x 1

� 2x 2

�,�

y 1� 2

y 2�

�iii

v.M

idpo

int

of a

Seg

men

t on

a N

um

ber

Lin

e

2.F

ill

in t

he

step

s to

cal

cula

te t

he

dist

ance

bet

wee

n t

he

poin

ts M

(4,�

3) a

nd

N(�

2,7)

.

Let

(x 1

,y1)

�(4

,�3)

.Th

en (

x 2,y

2) �

(,

).

d�

��

��

�(

�)2

�(

�)2

MN

��

��

�(

�)2

�(

�)2

MN

��

�(

)2�

()2

MN

��

��

MN

��

Fin

d a

deci

mal

app

roxi

mat

ion

for

MN

to t

he

nea

rest

hu

ndr

edth

.11

.66

Hel

pin

g Y

ou

Rem

emb

er

3.A

goo

d w

ay t

o re

mem

ber

a n

ew f

orm

ula

in

mat

hem

atic

s is

to

rela

te i

t to

on

e yo

u a

lrea

dykn

ow.I

f yo

u f

orge

t th

e D

ista

nce

For

mu

la,h

ow c

an y

ou u

se t

he

Pyt

hag

orea

n T

heo

rem

to

fin

d th

e di

stan

ce d

betw

een

tw

o po

ints

on

a c

oord

inat

e pl

ane?

Sam

ple

an

swer

:If

th

ese

gm

ent

det

erm

ined

by

the

po

ints

is n

eith

er h

ori

zon

tal n

or

vert

ical

,dra

wa

rig

ht

tria

ng

le t

hat

has

th

e se

gm

ent

as it

s hy

po

ten

use

.Th

e h

ori

zon

tal

sid

e w

ill h

ave

len

gth

|x2

�x 1

|an

d t

he

vert

ical

sid

e w

ill h

ave

len

gth

|y 2

�y 1

|.By

the

Pyt

hag

ore

an T

heo

rem

,d2

�|x 2

�x 1

|2�

|y 2�

y 1|2

�

(x 2�

x 1)2

�(y 2

�y 1

)2 .

136

100

36

10�

6

�3

74

�2

y 1y 2

x 1x 2

7�

2

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Geo

met

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Len

gth

s o

n a

Gri

dE

ven

ly-s

pace

d h

oriz

onta

l an

d ve

rtic

al l

ines

for

m a

gri

d.

You

can

eas

ily

fin

d se

gmen

t le

ngt

hs

on

a gr

id i

f th

e en

dpoi

nts

are

gri

d-li

ne

inte

rsec

tion

s.F

or h

oriz

onta

l or

ver

tica

lse

gmen

ts,s

impl

y co

un

t sq

uar

es.F

or

diag

onal

seg

men

ts,u

se t

he

Pyt

hag

orea

nT

heo

rem

(pr

oven

in

Ch

apte

r 7)

.Th

is

theo

rem

sta

tes

that

in

an

y ri

ght

tria

ngl

e,if

th

e le

ngt

h o

f th

e lo

nge

st s

ide

(th

e si

deop

posi

te t

he

righ

t an

gle)

is

can

d th

e tw

osh

orte

r si

des

hav

e le

ngt

hs

aan

d b,

then

c2

�a2

�b2

.

Fin

d t

he

mea

sure

of

E �F�

on t

he

grid

at

the

righ

t.L

ocat

e a

righ

t tr

ian

gle

wit

h E �

F�as

its

lo

nge

st s

ide.

EF

��

22�

5�

2 ��

29��

5.4

un

its

Fin

d e

ach

mea

sure

to

the

nea

rest

ten

th o

f a

un

it.

1.I�J�

32.

M�N�

73.

R�S�

4.2

4.Q�

S�5.

8

5.I�K�

7.6

6.J�K�

57.

L�M�

4.1

8.L�

N�7.

2

Use

th

e gr

id a

bov

e.F

ind

th

e p

erim

eter

of

each

tri

angl

e to

th

e n

eare

st t

enth

of

a u

nit

.

9.�

AB

C20

.210

.�

QR

S18

11.

�D

EF

16.6

12.

�L

MN

18.3

An

swer

s sh

ow

n a

re f

ou

nd

by

rou

nd

ing

seg

men

t le

ng

ths

bef

ore

ad

din

g.

13.O

f al

l th

e se

gmen

ts s

how

n o

n t

he

14.O

n t

he

grid

,1 u

nit

�0.

5 cm

.How

can

th

e

grid

,wh

ich

is

lon

gest

? W

hat

is

its

answ

ers

abov

e be

use

d to

fin

d th

e m

easu

res

len

gth

?B

C�

8.1

in c

enti

met

ers?

D

ivid

e by

2 o

r m

ulti

ply

by

0.5.

15.U

se y

our

answ

er f

rom

exe

rcis

e 8

to16

.Use

a c

enti

met

er r

ule

r to

fin

d th

e pe

rim

eter

ca

lcu

late

th

e le

ngt

h o

f se

gmen

t L

Nof

tri

angl

e IJ

Kto

th

e n

eare

st t

enth

of

a

in c

enti

met

ers.

Ch

eck

by m

easu

rin

gce

nti

met

er.

7.8

cmw

ith

a c

enti

met

er r

ule

r.3.

6 cm

E 2

5F

A B F

I J

KN

M

C

D

E

S

R Q L

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-3

1-3

Exam

ple

Exam

ple



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

An

gle

Mea

sure

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-4

1-4

©G

lenc

oe/M

cGra

w-H

ill19

Gle

ncoe

Geo

met

ry

Lesson 1-4

Mea

sure

An

gle

sIf

tw

o n

onco

llin

ear

rays

hav

e a

com

mon

en

dpoi

nt,

they

for

m a

n a

ngl

e.T

he

rays

are

th

e si

des

of t

he

angl

e.T

he

com

mon

en

dpoi

nt

is t

he

vert

ex.T

he

angl

e at

th

e ri

ght

can

be

nam

ed a

s �

A,�

BA

C,�

CA

B,o

r �

1.

A r

igh

t an

gle

is a

n a

ngl

e w

hos

e m

easu

re i

s 90

.An

acu

te a

ngl

eh

as m

easu

re l

ess

than

90.

An

ob

tuse

an

gle

has

mea

sure

gre

ater

th

an 9

0 bu

t le

ss t

han

180

.

AC

B

1

a.N

ame

all

angl

es t

hat

hav

e R

as a

vert

ex.

Th

ree

angl

es a

re �

1,�

2,an

d �

3.F

orot

her

an

gles

,use

th

ree

lett

ers

to n

ame

them

:�S

RQ

,�P

RT

,an

d �

SR

T.

b.

Nam

e th

e si

des

of

�1.

RS

� �� ,

RP

��

SR

T

PQ

12

3

Mea

sure

eac

h a

ngl

e an

dcl

assi

fy i

t as

rig

ht,

acu

te,o

r ob

tuse

.

a.�

AB

DU

sin

g a

prot

ract

or,m

�A

BD

�50

.50

�90

,so

�A

BD

is a

n a

cute

an

gle.

b.

�D

BC

Usi

ng

a pr

otra

ctor

,m�

DB

C�

115.

180

�11

5 �

90,s

o �

DB

Cis

an

obt

use

angl

e.

c.�

EB

CU

sin

g a

prot

ract

or,m

�E

BC

�90

.�

EB

Cis

a r

igh

t an

gle.

BA

DE

C

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

Ref

er t

o th

e fi

gure

.

1.N

ame

the

vert

ex o

f �

4.B

2.N

ame

the

side

s of

�B

DC

.D

B��

� ,D

C��

�

3.W

rite

an

oth

er n

ame

for

�D

BC

.�

3 o

r �

CB

D

Mea

sure

eac

h a

ngl

e in

th

e fi

gure

an

d c

lass

ify

it a

s ri

ght,

acu

te,o

r ob

tuse

.

4.�

MP

R12

0;o

btu

se

5.�

RP

N90

;ri

gh

t

6.�

NP

S45

;ac

ute

P

NM

R

S

C

BA

12

34

D

©G

lenc

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w-H

ill20

Gle

ncoe

Geo

met

ry

Co

ng

ruen

t A

ng

les

An

gles

th

at h

ave

the

sam

e m

easu

re a

re

con

gru

ent

angl

es.A

ray

th

at d

ivid

es a

n a

ngl

e in

to t

wo

con

gru

ent

angl

es i

s ca

lled

an

an

gle

bis

ecto

r.In

th

e fi

gure

,PN

� ��

is t

he

angl

e bi

sect

or o

f �

MP

R.P

oin

t N

lies

in

th

e in

teri

or o

f �

MP

Ran

d �

MP

N�

�N

PR

. Ref

er t

o th

e fi

gure

ab

ove.

If m

�M

PN

�2x

�14

an

d

m�

NP

R�

x�

34,f

ind

xan

d f

ind

m�

MP

R.

Sin

ce P

N� �

�bi

sect

s �

MP

R,�

MP

N�

�N

PR

,or

m�

MP

N�

m�

NP

R.

2x�

14 �

x�

34m

�N

PR

�(2

x�

14)

�(x

�34

)2x

�14

�x

�x

�34

�x

�54

�54

x�

14 �

34�

108

x�

14 �

14 �

34 �

14x

�20

QS

� ��

bis

ects

�P

QT

,an

d Q

P��

�an

d Q

R��

�ar

e op

pos

ite

rays

.

1.If

m�

PQ

T�

60 a

nd

m�

PQ

S�

4x�

14,f

ind

the

valu

e of

x.

4

2.If

m�

PQ

S�

3x�

13 a

nd

m�

SQ

T�

6x�

2,fi

nd

m�

PQ

T.

56

BA

��

and

BC

��

are

opp

osit

e ra

ys,B

F��

�b

isec

ts �

CB

E,a

nd

B

D� �

�b

isec

ts �

AB

E.

3.If

m�

EB

F�

6x�

4 an

d m

�C

BF

�7x

�2,

fin

d m

�E

BC

.

80

4.If

m�

1 �

4x�

10 a

nd

m�

2 �

5x,f

ind

m�

2.

50

5.If

m�

2 �

6y�

2 an

d m

�1

�8y

�14

,fin

d m

�A

BE

.

100

6.Is

�D

BF

a ri

ght

angl

e? E

xpla

in.

Yes;

sin

ce B

D��

�an

d B

F��

� are

bis

ecto

rs,m

�2

�m

�3

mu

st e

qu

al h

alf

the

tota

l an

gle

mea

sure

,an

d h

alf

of

180

is 9

0.

BA

CF

ED

12

34

QP

R

TS

PR

NM

Stu

dy G

uid

e a

nd I

nte

rven

tion

(con

tinued

)

An

gle

Mea

sure

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-4

1-4

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

An

gle

Mea

sure

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-4

1-4

©G

lenc

oe/M

cGra

w-H

ill21

Gle

ncoe

Geo

met

ry

Lesson 1-4

For

Exe

rcis

es 1

–12,

use

th

e fi

gure

at

the

righ

t.

Nam

e th

e ve

rtex

of

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1-4

1-4



An

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1-4

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Lesson 1-4

Pre-

Act

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ow b

ig i

s a

deg

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Rea

d th

e in

trod

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to

Les

son

1-4

at

the

top

of p

age

29 i

n y

our

text

book

.•

A s

emic

ircl

e is

hal

f a

circ

le.H

ow m

any

degr

ees

are

ther

e in

a

sem

icir

cle?

180

•H

ow m

any

degr

ees

are

ther

e in

a q

uar

ter

circ

le?

90

Rea

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g t

he

Less

on

1.M

atch

eac

h d

escr

ipti

on i

n t

he

firs

t co

lum

n w

ith

on

e of

th

e te

rms

in t

he

seco

nd

colu

mn

.S

ome

term

s in

th

e se

con

d co

lum

n m

ay b

e u

sed

mor

e th

an o

nce

or

not

at

all.

a.a

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re m

ade

up

of t

wo

non

coll

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r ra

ys w

ith

a1.

vert

ex

com

mon

en

dpoi

nt

42.

angl

e bi

sect

orb

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wh

ose

degr

ee m

easu

res

are

less

th

an 9

08

3.op

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te r

ays

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th

at h

ave

the

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e be

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0 an

d 18

05

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gles

e.a

tool

use

d to

mea

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an

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106.

con

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ent

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esf.

the

com

mon

en

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nt

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he

rays

th

at f

orm

an

an

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17.

righ

t an

gles

g.a

ray

that

div

ides

an

an

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into

tw

o co

ngr

uen

t an

gles

28.

acu

te a

ngl

es9.

com

pass

10.p

rotr

acto

r2.

Use

th

e fi

gure

to

nam

e ea

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f th

e fo

llow

ing.

a.a

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t an

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BE

or

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b.

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r �

AB

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an a

cute

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BF

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BC

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d.

a po

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in t

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rior

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BC

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a po

int

in t

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rior

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emb

er3.

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ive

som

e si

mil

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ces

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and

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ple

an

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men

ts a

nd

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e al

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bec

ause

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lve

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ure

s w

ith

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e sa

me

mea

sure

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iffe

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t b

ecau

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on

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men

ts h

ave

the

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ivid

-ed

in

to 6

0 m

inu

tes

(�),

and

each

min

ute

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an a

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e is

di

vide

d in

to 6

0 se

con

ds (

).

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ple

men

tary

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the

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0�.

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d t

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ple

men

t of

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h o

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m o

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180

�.F

ind

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ent

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ach

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the

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1-4

1-4



Stu

dy G

uid

e a

nd I

nte

rven

tion

An

gle

Rel

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nsh

ips

NA

ME

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____

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AT

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1-5

1-5

©G

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Lesson 1-5

Pair

s o

f A

ng

les

Ad

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nt

angl

esar

e an

gles

in

th

e sa

me

plan

e th

at h

ave

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mm

onve

rtex

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d a

com

mon

sid

e,bu

t n

o co

mm

on i

nte

rior

poi

nts

.Ver

tica

l an

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are

two

non

adja

cen

t an

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for

med

by

two

inte

rsec

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nes

.A p

air

of a

djac

ent

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es w

hos

en

onco

mm

on s

ides

are

opp

osit

e ra

ys i

s ca

lled

a l

inea

r p

air.

Iden

tify

eac

h p

air

of a

ngl

es a

s a

dja

cen

t a

ngl

es,v

erti

cal

an

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,an

d/o

r as

a l

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r p

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.

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ple

Exam

ple

a.

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and

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e a

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ide,

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oin

ts.T

hey

are

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.

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and

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56

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re v

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cal

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2 an

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4 ar

e al

so v

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and

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sum

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hey

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and

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sum

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to

the

figu

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ght.

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8.F

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the

ir m

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8.36

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Perp

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are

perp

endi

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th

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gure

at

the

righ

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per

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)

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1-5

1-5

Exam

ple

Exam

ple

Exer

cises

Exer

cises



An

swer

s

Skil

ls P

ract

ice

An

gle

Rel

atio

nsh

ips

NA

ME

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____

____

____

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1-5

1-5

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ill27

Gle

ncoe

Geo

met

ry

Lesson 1-5

For

Exe

rcis

es 1

–6,u

se t

he

figu

re a

t th

e ri

ght

and

a

pro

trac

tor.

1.N

ame

two

acu

te v

erti

cal

angl

es.

�E

KH

,�F

KG

2.N

ame

two

obtu

se v

erti

cal

angl

es.

�E

KF

,�H

KG

3.N

ame

a li

nea

r pa

ir.

Sam

ple

an

swer

:�

EK

H,�

EK

F

4.N

ame

two

acu

te a

djac

ent

angl

es.

�F

KG

,�G

KJ

5.N

ame

an a

ngl

e co

mpl

emen

tary

to

�E

KH

.�

GK

J

6.N

ame

an a

ngl

e su

pple

men

tary

to

�F

KG

.�

EK

Fo

r �

GK

H

7.F

ind

the

mea

sure

s of

an

an

gle

and

its

com

plem

ent

if o

ne

angl

e m

easu

res

18 d

egre

esm

ore

than

th

e ot

her

.36

,54

8.T

he

mea

sure

of

the

supp

lem

ent

of a

n a

ngl

e is

36

less

th

an t

he

mea

sure

of

the

angl

e.F

ind

the

mea

sure

s of

th

e an

gles

.72

,108

ALG

EBR

AF

or E

xerc

ises

9–1

0,u

se t

he

figu

re a

t th

e ri

ght.

9.If

m�

RT

S�

8x�

18,f

ind

xso

th

at T

R��

�⊥

TS

�� .

9

10.I

f m

�P

TQ

�3y

�10

an

d m

�Q

TR

�y,

fin

d y

so t

hat

�

PT

Ris

a r

igh

t an

gle.

25

Det

erm

ine

wh

eth

er e

ach

sta

tem

ent

can

be

assu

med

fr

om t

he

figu

re.E

xpla

in.

11.�

WZ

Uis

a r

igh

t an

gle.

Yes;

it is

mar

ked

wit

h a

rig

ht

ang

le s

ymb

ol.

12.�

YZ

Uan

d �

UZ

V a

re s

upp

lem

enta

ry.

Yes;

the

sum

of

thei

r m

easu

res

is 1

80 s

ince

th

e an

gle

s fo

rm a

lin

ear

pai

r.

13.�

VZ

Uis

adj

acen

t to

�Y

ZX

.

No

;th

e an

gle

s d

o n

ot

shar

e a

com

mo

n s

ide.

ZX

W

V

Y

U

TP

QR

S

K

G

J

FE H

©G

lenc

oe/M

cGra

w-H

ill28

Gle

ncoe

Geo

met

ry

For

Exe

rcis

es 1

–4,u

se t

he

figu

re a

t th

e ri

ght

and

a

pro

trac

tor.

1.N

ame

two

obtu

se v

erti

cal

angl

es.

Sam

ple

an

swer

:�

GF

H,�

CF

E2.

Nam

e a

lin

ear

pair

wh

ose

vert

ex i

s B

.�

GB

C,�

CB

A

3.N

ame

an a

ngl

e n

ot a

djac

ent

to b

ut

com

plem

enta

ry t

o �

FG

C.

�F

ED

4.N

ame

an a

ngl

e ad

jace

nt

and

supp

lem

enta

ry t

o �

DC

B.

�B

CG

or

�D

CH

5.T

wo

angl

es a

re c

ompl

emen

tary

.Th

e m

easu

re o

f on

e an

gle

is 2

1 m

ore

than

tw

ice

the

mea

sure

of

the

oth

er a

ngl

e.F

ind

the

mea

sure

s of

th

e an

gles

.23

,67

6.If

a s

upp

lem

ent

of a

n a

ngl

e h

as a

mea

sure

78

less

th

an t

he

mea

sure

of

the

angl

e,w

hat

are

the

mea

sure

s of

th

e an

gles

?12

9,51

AL

GE

BR

AF

or E

xerc

ises

7–8

,use

th

e fi

gure

at

the

righ

t.

7.If

m�

FG

E�

5x�

10,f

ind

xso

th

at

FC

� ��

⊥A

E��

� .16

8.If

m�

BG

C�

16x

�4

and

m�

CG

D�

2x�

13,

fin

d x

so t

hat

�B

GD

is a

rig

ht

angl

e.4.

5

Det

erm

ine

wh

eth

er e

ach

sta

tem

ent

can

be

assu

med

fro

m t

he

figu

re.E

xpla

in.

9.�

NQ

Oan

d �

OQ

Par

e co

mpl

emen

tary

.

No

;m

�N

QP

is n

ot

kno

wn

to

be

90.

10.�

SR

Qan

d �

QR

Pis

a l

inea

r pa

ir.

Yes;

they

are

ad

jace

nt

ang

les

wh

ose

no

nco

mm

on

sid

es a

re o

pp

osi

te r

ays.

11.�

MQ

Nan

d �

MQ

Rar

e ve

rtic

al a

ngl

es.

No

;th

e an

gle

s ar

e ad

jace

nt.

12.S

TREE

T M

APS

Dar

ren

ske

tch

ed a

map

of

the

cros

s st

reet

s n

eare

st

to h

is h

ome

for

his

fri

end

Mig

uel

.Des

crib

e tw

o di

ffer

ent

angl

ere

lati

onsh

ips

betw

een

th

e st

reet

s.

Sam

ple

an

swer

:B

eaco

n ⊥

Mai

n;

Oliv

e d

ivid

es t

wo

of

the

ang

les

form

ed b

y B

aco

n a

nd

Mai

n in

to p

airs

of

com

ple

men

tary

an

gle

s.

Oliv

e

Beacon

Main

Q

O

P

RS

M

N

GF

AB

E

D

C

DA

E

HG

BC

F

Pra

ctic

e (

Ave

rag

e)

An

gle

Rel

atio

nsh

ips

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-5

1-5



Readin

g t

o L

earn

Math

em

ati

csA

ng

le R

elat

ion

ship

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-5

1-5

©G

lenc

oe/M

cGra

w-H

ill29

Gle

ncoe

Geo

met

ry

Lesson 1-5

Pre-

Act

ivit

yW

hat

kin

ds

of a

ngl

es a

re f

orm

ed w

hen

str

eets

in

ters

ect?

Rea

d th

e in

trod

uct

ion

to

Les

son

1-5

at

the

top

of p

age

37 i

n y

our

text

book

.

•H

ow m

any

sepa

rate

ang

les

are

form

ed if

thr

ee li

nes

inte

rsec

t at

a c

omm

onpo

int?

(Do

not

use

an a

ngle

who

se in

teri

or in

clud

es p

art

of a

noth

er a

ngle

.)6

•H

ow m

any

sepa

rate

ang

les

are

form

ed if

nlin

es in

ters

ect

at a

com

mon

poin

t? (D

o no

t co

unt

an a

ngle

who

se in

teri

or in

clud

es p

art

of a

noth

er a

ngle

.)2n

Rea

din

g t

he

Less

on

1.N

ame

each

of

the

foll

owin

g in

th

e fi

gure

at

the

righ

t.

a.tw

o pa

irs

of c

ongr

uen

t an

gles

�1

and

�3,

�2

and

�4

b.

a pa

ir o

f ac

ute

ver

tica

l an

gles

�2

and

�4

c.a

pair

of

obtu

se v

erti

cal

angl

es�

1 an

d �

3d

.fo

ur

pair

s of

adj

acen

t an

gles

�1

and

�2,

�2

and

�3,

�3

and

�4,

�4

and

�1

e.tw

o pa

irs

of v

erti

cal

angl

es�

1 an

d �

3,�

2 an

d �

4f.

fou

r li

nea

r pa

irs

�1

and

�2,

�2

and

�3,

�3

and

�4,

�4

and

�1

g.fo

ur

pair

s of

su

pple

men

tary

an

gles

�1

and

�2,

�2

and

�3,

�3

and

�4,

�4

and

�1

2.T

ell

wh

eth

er e

ach

sta

tem

ent

is a

lway

s,so

met

imes

,or

nev

ertr

ue.

a.If

tw

o an

gles

are

adj

acen

t an

gles

,th

ey f

orm

a l

inea

r pa

ir.

som

etim

esb

.If

tw

o an

gles

for

m a

lin

ear

pair

,th

ey a

re c

ompl

emen

tary

.n

ever

c.If

tw

o an

gles

are

su

pple

men

tary

,th

ey a

re c

ongr

uen

t.so

met

imes

d.

If t

wo

angl

es a

re c

ompl

emen

tary

,th

ey a

re a

djac

ent.

som

etim

ese.

Wh

en t

wo

perp

endi

cula

r li

nes

in

ters

ect,

fou

r co

ngr

uen

t an

gles

are

for

med

.al

way

sf.

Ver

tica

l an

gles

are

su

pple

men

tary

.so

met

imes

g.V

erti

cal

angl

es a

re c

ompl

emen

tary

.so

met

imes

h.

Th

e tw

o an

gles

in

a l

inea

r pa

ir a

re b

oth

acu

te.

nev

eri.

If t

wo

angl

es f

orm

a l

inea

r pa

ir,o

ne

is a

cute

an

d th

e ot

her

is

obtu

se.

som

etim

es

3.C

ompl

ete

each

sen

ten

ce.

a.If

tw

o an

gles

are

su

pple

men

tary

an

d x

is t

he

mea

sure

of

one

of t

he

angl

es,t

hen

th

em

easu

re o

f th

e ot

her

an

gle

is

.

b.

If t

wo

angl

es a

re c

ompl

emen

tary

an

d x

is t

he

mea

sure

of

one

of t

he

angl

es,t

hen

th

em

easu

re o

f th

e ot

her

an

gle

is

.

Hel

pin

g Y

ou

Rem

emb

er4.

Loo

k u

p th

e n

onm

ath

emat

ical

mea

nin

g of

su

pple

men

tary

in y

our

dict

ion

ary.

How

can

this

def

init

ion

hel

p yo

u t

o re

mem

ber

the

mea

nin

g of

su

pple

men

tary

an

gles

?S

amp

lean

swer

:S

up

ple

men

tary

mea

ns

som

eth

ing

ad

ded

to

co

mp

lete

a t

hin

g.

An

an

gle

an

d it

s su

pp

lem

ent

can

be

join

ed t

o o

bta

in a

lin

ear

pai

r.

90 �

x

180

�x

65�

23

41

©G

lenc

oe/M

cGra

w-H

ill30

Gle

ncoe

Geo

met

ry

Cu

rve

Sti

tch

ing

Th

e st

ar d

esig

n a

t th

e ri

ght

was

cre

ated

by

a m

eth

od k

now

n a

s cu

rve

stit

chin

g.A

lth

ough

th

e de

sign

app

ears

to

con

tain

cu

rves

,it

is m

ade

up

enti

rely

of

lin

e se

gmen

ts.

To

begi

n t

he

star

des

ign

,dra

w a

60°

angl

e.M

ark

eigh

t eq

ual

ly-s

pace

d po

ints

on

eac

h r

ay,a

nd

nu

mbe

r th

e po

ints

as

show

n b

elow

.Th

en c

onn

ect

pair

s of

poi

nts

th

at h

ave

the

sam

e n

um

ber.

To

mak

e a

com

plet

e st

ar,m

ake

the

sam

e de

sign

in

si

x 60

°an

gles

th

at h

ave

a co

mm

on c

entr

al v

erte

x.

1.C

ompl

ete

the

sect

ion

of

the

star

des

ign

abo

ve b

y co

nn

ecti

ng

pair

s of

poi

nts

th

at h

ave

the

sam

e n

um

ber.

2.C

ompl

ete

the

foll

owin

g de

sign

.

3.C

reat

e yo

ur

own

des

ign

.You

may

use

sev

eral

an

gles

,an

d th

e an

gles

may

ove

rlap

.S

ee s

tud

ents

’wo

rk.

12

34

56

78

9

11

11

12

13

14

15

16

17

18

19

1

2

3

4

5

6

7

8

9

1213

1415

1617

1819

8

7

6

5

4

3

2

1

12

34

56

78

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-5

1-5



An

swer

s


Stu

dy G

uid

e a

nd I

nte

rven

tion

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-6

1-6

©G

lenc

oe/M

cGra

w-H

ill31

Gle

ncoe

Geo

met

ry

Lesson 1-6

Poly

go

ns

A p

olyg

onis

a c

lose

d fi

gure

for

med

by

a fi

nit

e n

um

ber

of c

opla

nar

lin

ese

gmen

ts.T

he

side

s th

at h

ave

a co

mm

on e

ndp

oin

t m

ust

be

non

coll

inea

r an

d ea

ch s

ide

inte

rsec

ts e

xact

ly t

wo

oth

er s

ides

at

thei

r en

dpoi

nts

.A p

olyg

on i

s n

amed

acc

ordi

ng

to i

tsn

um

ber

of s

ides

.A r

egu

lar

pol

ygon

has

con

gru

ent

side

s an

d co

ngr

uen

t an

gles

.A p

olyg

onca

n b

e co

nca

veor

con

vex.

Nam

e ea

ch p

olyg

on b

y it

s n

um

ber

of

sid

es.T

hen

cla

ssif

y it

as

con

cave

or c

onve

xan

d r

egu

lar

or i

rreg

ula

r.

Exam

ple

Exam

ple

a.

Th

e po

lygo

n h

as 4

sid

es,s

o it

is

a qu

adri

late

ral.

It i

s co

nca

ve b

ecau

se p

art

of D �

E�or

E�F�

lies

in

th

ein

teri

or o

f th

e fi

gure

.Bec

ause

it

is c

onca

ve,i

tca

nn

ot h

ave

all

its

angl

es c

ongr

uen

t an

d so

it

isir

regu

lar.

c.

Th

e po

lygo

n h

as 5

sid

es,s

o it

is

a pe

nta

gon

.It

isco

nve

x.A

ll s

ides

are

con

gru

ent

and

all

angl

es a

reco

ngr

uen

t,so

it

is a

reg

ula

r pe

nta

gon

.

DF

GEb

.

Th

e fi

gure

is

not

clo

sed,

so i

t is

not

a p

olyg

on.

d.

Th

e fi

gure

has

8 c

ongr

uen

t si

des

and

8 co

ngr

uen

t an

gles

.It

isco

nve

x an

d is

a r

egu

lar

octa

gon

.

H

JK

LI

Exer

cises

Exer

cises

Nam

e ea

ch p

olyg

on b

y it

s n

um

ber

of

sid

es.T

hen

cla

ssif

y it

as

con

cave

or c

onve

xan

d r

egu

lar

or i

rreg

ula

r.

1.2.

3.

hex

ago

n;

conv

ex;

qu

adri

late

ral;

conv

ex;

pen

tag

on

;co

nca

ve;

reg

ula

rir

reg

ula

rir

reg

ula

r

4.5.

6.

tria

ng

le;

conv

ex;

pen

tag

on

;co

nca

ve;

oct

ago

n;

con

cave

;ir

reg

ula

rir

reg

ula

rir

reg

ula

r

©G

lenc

oe/M

cGra

w-H

ill32

Gle

ncoe

Geo

met

ry

Peri

met

erT

he

per

imet

erof

a p

olyg

on i

s th

e su

m o

f th

e le

ngt

hs

of a

ll t

he

side

s of

th

epo

lygo

n.T

her

e ar

e sp

ecia

l fo

rmu

las

for

the

peri

met

er o

f a

squ

are

or a

rec

tan

gle.

Wri

te a

n e

xpre

ssio

n o

r fo

rmu

la f

or t

he

per

imet

er o

f ea

ch p

olyg

on.

Fin

d t

he

per

imet

er.

Stu

dy G

uid

e a

nd I

nte

rven

tion

(con

tinued

)

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

1-6

1-6

Exam

ple

Exam

ple

a.

P�

a�

b�

c�

3 �

4 �

5�

12 i

n.

b.

P�

4s�

4(5)

�20

cm

c.

P�

2 ��

2w�

2(3)

�2(

2)�

10 f

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Chapter 1 Assessment Answer Key Form 1 Form 2APage 37 Page 38 Page 39

(continued on the next page)

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

D

A

B

C

D

A

A

C

A

B

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

B

A

D

D

B

C

A

D

D

B

12 yd

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

B

D

C

A

B

C

C

C

A

B


Chapter 1 Assessment Answer KeyForm 2A (continued) Form 2BPage 40 Page 41 Page 42

An

swer

s

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

C

A

C

C

B

D

B

A

B

A

32

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

B

D

D

A

C

B

A

D

C

B

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

A

B

D

C

D

A

B

C

C

C

64


Chapter 1 Assessment Answer KeyForm 2CPage 43 Page 44

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Sample answer:DE��

A, B, C

AB��

Sample answer:D, E, C

6.3 cm

0.5 mm

7.3 cm

27 cm

3 in.

�58��32

�, ��52

��

(�1, �3)

15 � 5�5�

x � 8, y � 7

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

64°, acute

6

5

11

108

68

6

hexagon, convex,regular

174

35

21

length � 11;width � 4


Chapter 1 Assessment Answer KeyForm 2DPage 45 Page 46

An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Sample answer:TU��

Sample answer:T, U, V

RS��

Sample answer:X, Y, Z

1�12

� in.

�14

� in.

5.7 cm

17 cm

7

�65�

�3�12

�, 0�

(1, �1)

10 � �90� � �250�or 10 � 8�10� �

35.3 units

2

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B:

135°, obtuse

6

6

7

122

32

9

pentagon,convex, regular

185

51

68

10, 18, 9


Chapter 1 Assessment Answer KeyForm 3Page 47 Page 48

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

planes ABCD,BFCE, FBA, CDE,

and plane P orADEF

DC�� or BC��

AE��

1�14

� in.

�18

� in.

12.3 cm and 19.3 cm

6

8

�20� or 2�5� � 4.5

��2, ��12

��,(�4, �1.5)

y � 2, y � �4

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

3

15.5 � x � 8

27

36

8

8.5

quadrilateral,concave, irregular

9 � �5� � 3�10�� 20.7

39

square: 9,triangle: 12

x

y

O

BC

D

A

Chapter 1 Assessment Answer KeyPage 49, Open-Ended Assessment

Scoring Rubric


Score General Description Specific Criteria

• Shows a thorough understanding of concepts involvingspecial angle relationships, classification of angles,distance formula, regular polygons, angle bisectors, andperimeters.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs and figures are accurate and appropriate.• Goes beyond requirements of some or all problems.

• Shows an understanding of the concepts involving specialangle relationships, classification of angles, distanceformula, regular polygons, angle bisectors, and perimeters.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs and figures are mostly accurate and appropriate.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts involvingspecial angle relationships, classification of angles,distance formula, regular polygons, angle bisectors, andperimeters.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs and figures are mostly accurate.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Graphs and figures may be accurate but lack detail or

explanation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of most of the conceptsinvolving special angle relationships, classification ofangles, distance formula, regular polygons, anglebisectors, and perimeters.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs and figures are inaccurate or inappropriate.• Does not satisfy requirements of most problems.• No answer may be given.

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

4 SuperiorA correct solution that is supported by well-developed, accurateexplanations

An

swer

s


Chapter 1 Assessment Answer KeyPage 49, Open-Ended Assessment

Sample Answers

1.

points A, B, and C

2a. After drawing a line on a coordinategrid, students should label two pointson the graph D and G.

b. The students should use either thePythagorean Theorem, the DistanceFormula, or the Midpoint Formula todetermine the distance between pointsD and G.

c. Using the Midpoint Formula and theknown coordinates for points D(x1, y1)and G(x2, y2), the coordinates of pointH(x, y) can be found by solving for x

and y in �x �

2x1

� � x2 and �y �

2y1

� � y2.

3a. The student draws a rectangle, labelsthe vertices W, X, Y, and Z, labels thewidth with a variable, such as x, andthe length in terms of that variable,3x � 5.

b. An expression for the perimeter, where x is the width, would be either 2(3x � 5) � 2x or 8x � 10.

c. Solving 58 � 8x � 10 for x, the width isfound to be 6 mm. To check that thisanswer is correct, use the value of thewidth to determine the length, 23. Thesum of all four sides, 23 � 23 � 6 � 6,should equal 58.

d. After using a ruler to draw a segmentthat is 23 mm long, students shouldlabel the endpoints P and Q.

e. A measurement of 23 mm for P�Q� isaccurate to within 0.5 mm. So, ameasurement of 23 mm could be 22.5 to23.5 mm.

4a. After drawing an acute angle, the studentlabels the vertex B and point A on oneray and point C on the other ray. Thenthe student uses a protractor to find themeasure of �ABC. The student lets themeasure of �ABC equal (6x � 1) andsolves for x.

b. To find the measure of an angle that iscomplementary to �ABC, you wouldsubtract m�ABC from 90.

c. To find the measure of an angle that issupplementary to �ABC, you wouldsubtract m�ABC from 180.

5a.

b. If RS�� is an angle bisector, then m�TRSand m�SRU must be equal. Therefore,solve 4x � 6 � 8x � 6 for x.4x � 6 � 8x � 66 � 6 � 8x � 4x Add 6 and subtract 4x from

each side.

12 � 4x Combine like terms.

3 � x Divide each side by 4.

c. When x � 7.5, m�TRS � 4(7.5) � 6 andm�SRU � 8(7.5) � 6. Simplifying eachexpression results in m�TRS � 36 andm�SRU � 8(7.5) � 6 � 54. Since thesum of the two measures is 90, RU�� andRT�� must be perpendicular.

U

S

T

R

(4x � 6)�

(8x � 6)�

R

s

BC

A

In addition to the scoring rubric found on page A25, the following sample answers may be used as guidance in evaluating open-ended assessment items.


Chapter 1 Assessment Answer KeyVocabulary Test/Review Quiz 1 Quiz 3Page 50 Page 51 Page 52

An

swer

s

Quiz 2Page 51

Quiz 4Page 52

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

perpendicular

complementary

angle

midpoint

vertical angles

angle bisector

supplementary

adjacent angles

acute angle

congruent

Sample answer: Sincethe measuring tool is

divided into �12

�-inch

increments, themeasurement isprecise to within

�14

� inch.

Sample answer: Point

M is between points Pand Q only if P, Q, and

M are collinear andPM � MQ � PQ.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

RS��, or RU�� or SU��

point Spoints R, S, U or

points T, S, V

1�14

� in.

�18

� inch

8.9 cm

3

33 in.

4

C

1.

2.

3.

4.

5.

(4, 7)(3, �2)

14

40

B

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

TobtuseU or V

23Sample answer:

�TSU and �USV�TSU and �WSP or

�TSP and �USW

19

12

25

B

1.

2.

3.

4.

5.

Sample answer:

14 m

86 units

The perimeter isdoubled.

4


Chapter 1 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 53 Page 54

Part I

Part II

6.

7.

8.

9.

10.

�37�

��12

�, �1�(0, 3)

3

74 units

1.

2.

3.

4.

5.

B

C

B

C

D

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

A, C, and E or B, D, and F

C

3 cm

10 mm

26 units

B (�7, 1)

vertex: N; sides: NJ��

and NK��; 90�; right

vertex: N; sides: NK��

and NH��; 100�; obtuse

�AFB and �FCD or �EFG and �FCD or

�CFD and �CDG

�AFE and �BFD

�AFB or �EFG

7

quadrilateral;concave; irregular

10 � �50� � 17.1 units

18 cm


Chapter 1 Assessment Answer KeyStandardized Test Practice

Page 55 Page 56

An

swer

s

Chapter 1 Assessment Answer KeyStandardized Test Practice

Page 55 Page 56

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. E F G H

A B C D

E F G H

A B C D

E F G H

A B C D

E F G H

A B C D

E F G H

A B C D 11. 12.

13. 14.

15.

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

16.

17.

18.

20 units

81.5 units

21 units

2 8 . 9

1 1

5 5

2 0

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