1-1 Nets and Drawings for Visualizing Geometrymrroosmustangmath.weebly.com/uploads/3/1/7/3/31739055/chapter_1... · Visualizing Geometry 1-1 ... Triangles, rectangles, pentagons,

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Vocabulary

Review

Chapter 1 2

Nets and Drawings for Visualizing Geometry 1-1

Identify each figure as two-dimensional or three-dimensional.

1. 2. 3.

Vocabulary Builder

polygon (noun) PAHL ih gahn

Definition A polygon is a two-dimensional fi gure with three or more sides, where each side meets exactly two other sides at their endpoints.

Main Idea: A polygon is a closed fi gure, so all sides meet. No sides cross each other.

Examples: Triangles, rectangles, pentagons, hexagons, and octagons are polygons.

Use Your Vocabulary

Underline the correct word(s) to complete each sentence.

4. A polygon is formed by two / three or more straight sides.

5. A circle is / is not a polygon.

6. A triangle / rectangle is a polygon with three sides.

7. The sides of a polygon are curved / straight .

8. Two / Three sides of polygon meet at the same point.

Cross out the figure(s) that are NOT polygons.

9.

C

B

A

E

D

10. M

L

N

P

Q

11.

V

W U

SR

XT

cchh other

polygon

three-dimensional two-dimensional three-dimensional

HSM11GEMC_0101.indd 2HSM11GEMC_0101.indd 2 4/14/09 8:08:24 AM4/14/09 8:08:24 AM

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Problem 1

BB

HSM11_GEMC_0101_T93725

E

A B C

F

D

3 Lesson 1-1

Underline the correct word(s) to complete the sentence.

12. A net is a two-dimensional / three-dimensional diagram that you can fold to form

a two-dimensional / three-dimensional figure.

13. Circle the net that you can NOT fold into a cube.

HSM11_GMSE_0101_14057

HSM11_GMSE_0101_14058

HSM11_GMSE_0101_14059

Use the net of a cube at the right for Exercises 14 and 15.

14. Suppose you fold the net into a cube. What number will be opposite each face?

1 3 4

15. Suppose you fold the net into a cube. What number is missing from each view?

?

15

HSM11_GMSE_0101_14061

HSM11_GMSE_0101_14062

?

2

3

HSM11_GMSE_0101_14063

?

6 4

Identifying a Solid From a Net

Got It? The net at the right folds into the cube shown. Which letters will be on the top and right side of the cube?

16. Four of the five other letters will touch some side of Face B when the net is folded into a cube. Cross out the letter of the side that will NOT touch some side of Face B.

A C D E F

17. Which side of the cube will that letter be on? Circle your answer.

Top Bottom Right Left Back

18. Use the net. Which face is to the right of Face B? How do you know?

_______________________________________________________________________

_______________________________________________________________________

19. Use the net. Which face is on the top of the cube? How do you know?

_______________________________________________________________________

_______________________________________________________________________

HSM11_GMSE_0101_14060

1

3 4

6

5

2

C. Explanations may vary. Sample: The left side of C and the right

side of B are the same edge of the cube.

E. Answers may vary. Sample: E folds down to become the top of

the cube.

6

4

5

1

2

3

HSM12GEMC_0101.indd 3 4/29/11 9:55:42 AM

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Problem 2

Problem 3

10 cm10 cm

7 cm4 cm

Chapter 1 4

Drawing a Net From a Solid

Got It? What is a net for the figure at the right? Label the net with its dimensions.

Write T for true or F for false.

20. Three of the faces are rectangles.

21. Four of the faces are triangles.

22. The figure has five faces in all.

23. Now write a description of the net.

_______________________________________________________________________

_______________________________________________________________________

24. Circle the net that represents the figure above.

10 cm

10 cm

4 cm

7 cm

10 cm

10 cm

4 cm

7 cm

7 cm

7 cm 7 cm

10 cm10 cm

10 cm

Isometric Drawing

Got It? What is an isometric drawing of this cube structure?

25. The cube structure has

edges that you can see and

vertices that you can see.

26. The isometric dot paper shows 2 vertices and 1 edge of the cube structure. Complete the isometric drawing.

Answers may vary. Sample: The net has three rectangles and two

triangles that fold to form the figure above.

T

F

T

24

16


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Math Success

Now Iget it!

Need toreview

0 2 4 6 8 10

Problem 4

Lesson Check

Right

Front

5 Lesson 1-1

Check off the vocabulary words that you understand.

net isometric drawing orthographic drawing

Rate how well you can use nets, isometric drawings, and orthographic drawings.

Orthographic Drawing

Got It? What is the orthographic drawing for this isometric drawing?

27. Underline the correct word to complete the sentence.

If you built the figure out of cubes, you would use seven / eight cubes

28. Cross out the drawing below that is NOT part of the orthographic drawing. Then label each remaining drawing. Write Front, Right, or Top.

Vocabulary Tell whether each drawing is isometric, orthographic, a net, or none.

29. Write dot paper, one view, three views or none. Then label each figure.

Top

Front Right

Right

Front

Do you UNDERSTAND?

top

one view

right

three views

cross out

dot paper

front

none

net orthographic isometric none

HSM11GEMC_0101.indd 5HSM11GEMC_0101.indd 5 3/1/09 1:29:33 PM3/1/09 1:29:33 PM

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Vocabulary

Review

Points, Lines, and Planes 1-2

Chapter 1 6

Draw a line from each net in Column A to the three-dimensional figure it represents in Column B.

Column A Column B

1.

2.

3.

Vocabulary Builder

conjecture (noun, verb) kun JEK chur

Main Idea: A conjecture is a guess or a prediction.

Definition: A conjecture is a conclusion reached by using inductive reasoning.

Use Your Vocabulary

Write noun or verb to identify how the word conjecture is used in each sentence.

4. You make a conjecture that your volleyball team will win.

5. Assuming that your sister ate the last cookie is a conjecture.

6. You conjecture that your town will build a swimming pool. verb

noun

noun


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d.Key Concept Undefined and Defined Terms

Postulates 11, 12, 13, and 14

Undefined or Defined Term Diagram Name

point A

P

line

plane

segment

ray

opposite rays

AB

AB

AB

CA, CB

7 Lesson 1-2

Write the correct word from the list on the right. Use each word only once.

7.

8.

9.

10.

11.

12.

Draw a line from each item in Column A to its description in Column B.

Column A Column B

13. plane HGE intersection of AB and line z

14. BF plane AEH

15. plane DAE line through points F and E

16. line y intersection of planes ABF and CGF

17. point A plane containing points E, F, and G

18. Complete each postulate with line, plane, or point.

Postulate 1-1 Th rough any two points there is exactly one 9.

Postulate 1-2 If two distinct lines intersect, then they intersect in exactly one 9.

Postulate 1-3 If two distinct planes intersect, then they intersect in exactly one 9.

Postulate 1-4 Th rough any three noncollinear points there is exactly one 9.

lineopposite rays

planepointray

segment

G

H

y

EF

D

A

B z

C

x

7 Lesson 1-2

line

point

line

plane

A

A

B

A BP

C

A B

A B

BCA


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d.Problem 3

Problem 2

A

E F

GB

CD

H

Chapter 1 8

Naming Segments and Rays

Got It? Reasoning EF) and FE

) form a line. Are they opposite rays? Explain.

For Exercises 2529, use the line below.

E F

25. Draw and label points E and F. Then draw EF) in one color and FE

) in another color.

26. Do EF) and FE

) share an endpoint? Yes / No

27. Do EF) and FE

) form a line? Yes / No

28. Are EF) and FE

) opposite rays? Yes / No

29. Explain your answer to Exercise 28.

_______________________________________________________________________

_______________________________________________________________________

Finding the Intersection of Two Planes

Got It? Each surface of the box at the right represents part of a plane. What are the names of two planes that intersect in

*BF)?

30. Circle the points that are on *BF) or in one of the two planes.

A B C D E F G H

31. Circle another name for plane BFG. Underline another name for plane BFE.

ABF BCD BCG CDH FGH

32. Now name two planes that intersect in *BF).

Write P if the statement describes a postulate or U if it describes an undefined term.

19. A point indicates a location and has no size.

20. Through any two points there is exactly one line.

21. A line is represented by a straight path that has no thickness and extends in two opposite directions without end.

22. If two distinct planes intersect, then they intersect in exactly one line.

23. If two distinct lines intersect, then they intersect in exactly one point.

24. Through any three nontcollinear points there is exactly one plane.

U

P

P

P

P

U

Answers may vary. Sample: The rays point in opposite directions

but they do not share an endpoint.

ABE, ABF, BFE, AFE, BFC, BFG, CBG, and CFG.

Answers may vary. Accept any variation of


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Lesson Check

Now Iget it!

Need toreview

0 2 4 6 8 10

Math Success

Problem 4

MJ

N P

QRK

L

A B

9 Lesson 1-2

Do you UNDERSTAND?

Are AB) and BA

) the same ray? Explain.

Underline the correct symbol to complete each sentence.

36. The endpoint of AB) is A / B .

37. The endpoint of BA) is A / B .

38. Use the line. Draw and label points A and B. Then draw AB) and BA

).

39. Are AB) and BA

) the same ray? Explain.

_______________________________________________________________________


point line plane segment ray postulate axiom

Rate how well you understand points, lines, and planes.

Using Postulate 14

Got It? What plane contains points L, M, and N? Shade the plane.

33. Use the figure below. Draw LM , LN , and MN as dashed segments. Then shade plane LMN.

Underline the correct word to complete the sentence.

34. LM , LN , and MN form a triangle / rectangle .

35. Name the plane.

_______________________________________________________________________

M

J

N P

KR

Q

L

No. They point in opposite directions and have different endpoints.

Explanations may vary. Sample:

Answers may vary. Accept any of LMN, MNL, NLM, MLN, LNM, NML


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Vocabulary

Review

Chapter 1 10

1-3 Measuring Segments

Draw an example of each.

1. point 2. *AB) 3. DF

)

Vocabulary Builder

segment (noun) SEG munt

Definition: A segment is part of a line that consists of two endpoints and all points between them.

Main Idea: You name a segment by its endpoints.

Use Your Vocabulary

Complete each sentence with endpoint, endpoints, line, or points.

4. A ray has one 9.

5. A line contains infinitely many 9.

6. A segment has two 9.

7. A segment is part of a 9.

Place a check if the phrase describes a segment. Place an if it does not.

8. Earths equator

9. the right edge of a books cover 10. one side of a triangle

Every point on a line can be paired with a real number, called the coordinate of the point.

Postulate 15 Ruler Postulate

H J

segment HJ

endpoint

Answers may vary. Samples are shown.

points

endpoints

line

AA B D F


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d.Problem 1

Postulate 16 Segment Addition Postulate

If three points A, B, and C are collinear and B is between A and C, then AB 1 BC 5 AC .

Given points A, B, and C are collinear and B is between A and C, complete each equation.

13. AB5 5 and BC5 4, so AB1 BC 5 1 and AC 5 .

14. AC5 12 and BC5 7, so AC2 BC 5 2 and AB 5 .

Problem 2

J

4x 6 7x 15

K L

6 84 122 1626 0

VUS

4 10 14

11 Lesson 1-3

Measuring Segment Lengths

Got It? What are UV and SV on the number line?

11. Label each point on the number line with its coordinate.

12. Find UV and SV. Write a justification for each statement.

UV 5 P 2 P SV 5 P 2 P

UV 5 P P SV 5 P P

UV 5 SV 5

Using the Segment Addition Postulate

Got It? In the diagram, JL 5 120. What are JK and KL?

15. Write a justification for each statement.

JK 1 KL 5 JL

(4x 1 6) 1 (7x 1 15) 5 120

11x 1 21 5 120

11x 5 99

x 5 9

16. You know that JK 5 4x 1 6 and KL 5 7x 1 15. Use the value of x from Exercise 15 to to find JK and KL. Find JK and KL.

17. JK 5 and KL 5 .

24

24

4

14Definition of distance10 14

18

Subtract.

Find the absolute value.

218

5 4 9

12 7 5

Segment Addition Postulate

Simplify.

Subtract 21 from each side.

Divide each side by 11.

4(9) 1 6 5 36 1 6 5 42 and 7(9) 1 15 5 63 1 15 5 78

Substitute.

42 78


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Problem 3

A

6 4 2 0 2 4 6 8 10 12 14 16

B C D E

Chapter 1 12

Comparing Segment Lengths

Got It? Use the diagram below. Is AB congruent to DE?

In Exercises 18 and 19, circle the expression that completes the equation.

18. AB 5 j

22 2 2 u22 22 u u22 2 3 u u22 2 4 u

19. DE 5 j

3214 10114 u 5214 u u 10214 u

20. After simplifying, AB 5 and DE 5 .

21. Is AB congruent to DE? Explain.

_______________________________________________________________________

Th e midpoint of a segment is the point that divides the segment into two congruent segments.

Use the number line below for Exercises 2225.

42 31 53 25 4 0

JH IG KFEDCBA

1

22. Point is halfway between points B and J. 23. The midpoint of AE is point .

24. Point divides EK into two congruent segments.

25. Find the midpoint of each segment. Then write the coordinate of the midpoint.

AG DH AK

Midpoint

Coordinate

26. Find the coordinate of the midpoint of each segment.

segment with segment with endpoints at 24 and 2 endpoints at 22 and 4

Coordinate of midpoint

27. Circle the expression that relates the coordinate of the midpoint to the coordinates of the endpoints.

x11 x2

(x1 1 x2)2

(x1 2 x2)2

5 4

F

H

C

21 1

No. Segments with different lengths are not congruent.


D F F

0022


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d.Problem 4

8x 11

T U V12x 1

Lesson Check

P Q R S T

2 3 4 5 6

Math Success

Now Iget it!

Need toreview

0 2 4 6 8 10

13 Lesson 1-3

Using the Midpoint

Got It? U is the midpoint of TV . What are TU, UV, and TV?

28. Use the justifications at the right to complete the steps below.

Step 1 Find x.

TU 5 UV Defi nition of midpoint

8x 1 11 5 Substitute.

8x 1 11 1 5 1 Add 1 to each side.

5 Subtract 8x from each side.

5 x Divide each side by 4.

Step 2 Find TU and UV.

TU 5 8 ? 1 11 5 Substitute for x.

UV 5 12 ? 2 1 5 Substitute.

Step 3 Find TV.

TV 5 TU 1 UV Defi nition of midpoint

5 1 Substitute.

5 Simplify.

Do you UNDERSTAND?

Vocabulary Name two segment bisectors of PR.

Underline the correct word or symbol to complete each sentence.

29. A bisector / midpoint may be a point, line, ray, or segment.

30. The midpoint of PR is point P / Q / R .

31. Line passes through point P / Q / R .

32. Two bisectors of PR are and .


congruent segments coordinate midpoint segment bisector

Rate how well you can fi nd lengths of segments.

12x2 1

1 1

12 4x

3

3 3

3 35

35 35

70

WV ? Why or why not?

_______________________________________________________________________

Draw a line from each word in Column A to the angles it describes in Column B.

Column A Column B

10. supplementary /1 and /2

11. adjacent /2 and /3

12. vertical /2 and /5

13. complementary /3 and /6

FC)

FD)

Congruence marks are on TW and WV .



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Problem 4

Problem 3

Postulate 19 Linear Pair Postulate

PK

(2x 24) (4x 36)

J

L

Overmatter

Chapter 1 20

Finding Missing Angle Measures

Got It? Reasoning lKPL and lJPL are a linear pair, mlKPL 5 2x 1 24, and mlJPL 5 4x 1 36. How can you check that mlKPL 5 64 and mlJPL 5 116?

22. What is one way to check solutions? Place a in the box if the response is correct. Place an in the box if it is incorrect.

Draw a diagram. If it looks good, the solutions are correct.

Substitute the solutions in the original problem statement.

23. Use your answer(s) to Exercise 22 to check the solutions.

24. How does your check show that you found the correct angle measurements?

_______________________________________________________________________

_______________________________________________________________________

Using an Angle Bisector to Find Angle Measures

Got It? KM) bisects lJKL. If mlJKL 5 72, what is mlJKM ?

25. Write a justification for each step.

m/JKM 5 m/MKL

m/JKM 1 m/MKL 5 m/JKL

2m/JKM 5 m/JKL

m/JKM 5 12 m/JKL

If two angles form a linear pair, then they are supplementary.

21. If /A and /B form a linear pair, then m/A 1 m/B 5 .180

mlKPL 5 642x 1 24 5 64 2x 5 40 x 5 20

ml JPL 5 1164x 1 36 5 116 4x 5 80 x 5 20

Answers may vary. Sample: You solved correctly because you found

the same solution to both equations.

Definition of angle bisector

Angle Addition Postulate

Substitute.

Divide each side by 2.


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Lesson Check

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Math Success

L

M

K

36

36

J

4x

2x4x + 2x = 180

6x = 180x = 30

21 Lesson 1-5

Do you UNDERSTAND?

Error Analysis Your friend calculated the value of x below. What is her error?

28. Circle the best description of the largest angle in the figure.

acute obtuse right straight

29. Complete: 4x 1 2x 5

30. What is your friends error? Explain.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________


angle complementary supplementary angle bisector vertical

Rate how well you can fi nd missing angle measures.

26. Complete.

m/JKL 5 , so m/JKM 5 .

27. Now complete the diagram below.

72 36

90

Answers may vary. Sample: She thought a right angle measures 1808,

so she set the sum of the angle measures equal to 180.


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Vocabulary

Review

S

G

W

P

W

s

s

Basic Constructions 1-6

Chapter 1 22

Draw a line from each word in Column A to its symbol or picture in Column B.

Column A Column B

1. congruent

2. point

3. ray

4. vertex

5. intersection of segments O

Vocabulary Builder

perpendicular (adjective) pur pun DIK yoo lur

Definition: Perpendicular means at right angles to a given line or plane.

Example: Each corner of this paper is formed by perpendicular edges of the page.

Non-Examples: Acute, obtuse, and straight angles do not have perpendicular rays.

Use Your Vocabulary

6. Circle the figure that shows perpendicular segments.


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d.Problem 1

Problem 2

X

Y

R S

B

Step 4 Open the ? to the length ofAC. With the compass point on pointS, draw an ? . Label where this arcintersects the other arc as point T.

compass / arc

Step 6 Draw FR.

Step 1 Use a straightedge to constructa ray with endpoint F.

Step 3 Use the same compasssetting. Put the ? point on pointF. Draw a long ? and label itsintersection with the ray as S.

compass / arc

Step 5 Use the same compass setting.Put the ? point on point T. Draw an ? and label its intersection with the first ? as point R.

compass / arc / arc

Step 2 With your ? point on vertex B,draw a(n) ? that intersects both sides of B. Label the points of intersection A and C.

compass / arc

B

A

C

RT

SF

23 Lesson 1-6

Constructing Congruent Segments

Got It? Use a straightedge to draw XY . Then construct RS so that RS 5 2XY.

7. A student did the construction at the right. Describe each

step of the construction.

Step 1

Step 2

Step 3

Step 4

Step 5

Constructing Congruent Angles

Got It? Construct lF so that mlF 5 2mlB at the right.

8. Use arc or compass to complete the sentence(s) in each step. In the large box, construct /F .

Use a straightedge to draw XY .

Draw a ray with endpoint R.

Draw an arc with compass point

Draw another arc with the compass point at the intersection.

Label the point of intersection S.

at R and opening XY.


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d.

Problem 3

S T

S M T

Y

X

Chapter 1 24

A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint.

9. Circle the drawing that shows the perpendicular bisector of a segment.

A

E

FB

A

E

F B

A

E

FB

Constructing the Perpendicular Bisector

Got It? Draw ST . Construct its perpendicular bisector.

10. Error Analysis A students construction of the perpendicular bisector of ST is shown below. Describe the students error.

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

11. Do the construction correctly in the box below.

Answers may vary. Sample: The student did not make the opening

of the arc drawn from points S and T greater than 12ST.


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Lesson Check

Now Iget it!

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Math Success

Problem 4

Step 1 Put the compass point on vertex . Draw an arcthat intersects the sides of . Label the points of

intersection A and B.

Step 3 Draw .

Y

YP

Y

Step 2 Put the compass point on point A and draw an arc. With the same / a different

compass setting, draw an arc using point B. Be sure the arcs intersect. Label the point where the two arcs intersect P.

ZBY

X

A

P

25 Lesson 1-6

Do you UNDERSTAND?

Vocabulary What two tools do you use to make constructions?

Draw a line from each task in Column A to the tool used in Column B.

Column A Column B

13. measure lines compass

14. measure angles protractor

15. construct arcs ruler

16. construct lines straightedge


straightedge compass construction perpendicular bisector

Rate how well you can construct angles and bisectors.

Constructing the Angle Bisector

Got It? Draw obtuse lXYZ . Then construct its bisector YP).

12. Obtuse /XYZ is drawn in the box at the right. Complete the flowchart and do each step of the construction.


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Vocabulary

Review

x

y

O 4

4

24

4

B

A

C

G

DE

F

C

E F A

DB

x

y

8

510

Chapter 1 26

Midpoint and Distance in the Coordinate Plane1-7

Use the figure at the right for Exercises 16. Write T for true or F for false.

1. Points A and B are both at the origin.

2. If AB 5 BC , then B is the midpoint of AC .

3. The midpoint of AE is F.

4. The Pythagorean Theorem can be used for any triangle.

5. Point C is at (6, 0).

6. Point E has a y-coordinate of 28.

Vocabulary Builder

midpoint (noun) MID poynt

Definition: A midpoint of a segment is a point that divides the segment into two congruent segments.

Use Your Vocabulary

Use the figure at the right for Exercises 79.

7. The midpoint of EF is G( , ).

8. The midpoint of AB is ( , ), or the origin.

9. The midpoint of CD is ( , ).

F

F

F

T

F

F

0

0

0.5

0

2.5

0


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d.Key Concept Midpoint Formulas

Problem 2

2 4 6 8 10 12 14 16

2

4

(1, 2)

(17, 4)

( 4) 2

(1 ) 2

( , )

172

9 3

x

y

O

On a Number Line In the Coordinate Plane

Given A(x1, y1) and B(x2, y2), the coordinates of the

( ,x1 x22 )y1 y2

2midpoint of AB are M

The coordinate of the midpoint M of AB

.a b

2with endpoints at a and b is

Midpoint Formula Midpoint Coordinates

,( )4 9x1 1 3

2

y1 1 5

2,

9y1 1 5

25

18y1 1 5 5

13y1 5

4x1 1 3

25

8x1 1 3 5

11x1 5

Solve two equations.

( , )

Endpoint A Coordinates

3 5 ( )

27 Lesson 1-7

Finding an Endpoint

Got It? The midpoint of AB has coordinates (4, 29). Endpoint A has coordinates (23, 25). What are the coordinates of B?

15. Complete the equations below.

16. The coordinates of endpoint B are ( ).

Find the coordinate of the midpoint M of each segment with the given endpoints on a number line.

10. endpoints 5 and 9 11. endpoints 23 and 5

12. endpoints 210 and 23 13. endpoints 28 and 21

14. Complete the diagram below.

11, 13

7

26 12 24 12

1


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Problem 3

y2

y1

y2 y1

x1

x2 x1

x2O

y

x

d

B

A

a 2 b 2 c 2a

bc

y

8 4

4

8

53 2 (22) 5

x

6

1521 2 14 5

S(2, 14)

R(3, 1)

Chapter 1 28

Finding Distance

Got It? SR has endpoints S(22, 14) and R(3, 21). What is SR to the nearest tenth?

20. Complete the diagram at the right.

21. Let S(22, 14) be (x1, y1) and let R(3, 21) be (x2, y2) . Use the justifications and complete thesteps below to find SR.

d 5 Q 2 x1R2 1 Q 2 y1R2 Use the Distance Formula.

SR 5 Q 2 (22)R2 1 Q 2 14R2 Substitute.

5 Q R2 1 Q R2 Subtract.

5 1 Simplify powers.

5 Add.

< Use a calculator.

Formula The Distance Formula

Use the diagrams above. Draw a line from each triangle side in Column A to the corresponding triangle side in Column B.

Column A Column B

17. y2 2 y1 a

18. x2 2 x1 b

19. distance, d c

Th e distance between two points A(x1, y1) and B(x2, y2) is d 5 "(x2 2 x1)2 1 (y2 2 y1)2.Th e Distance Formula is based on the Pythagorean Th eorem.

y2

1

15

x2

3

5

25 225

250

15.8


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d.Problem 4

Math Success

Lesson Check

Now Iget it!

Need toreview

0 2 4 6 8 10

x

y

O103050 10

10

10

20

20

20 30 40 50

B

CA

D

E

F

x

y

O103050 10

10

10

20

20

20 30 40 50

B

CA

D

E

F

00000AAAAA 2222222000222002020202020222222202020

BBBBBBBBBBBB

AAAAAAAAFFFFFFF

OOOOOOOOOOOOOOOOO000000000000011111000000000000333333333 001

10000

10101000010000010000010000000000000

202020202000200000000000

2002000200

000000222 033 0400444444

CCCCCCCC

EEEEEEEEEEEEEEEEEEE

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO10000000000000000111111111113000000000000000033333333333333 100011

11111110010101010101010101010101

111011010110100101000100100101010101000101010101010101010000001000000101010

2202220202202020020202022020220200220020202020202020222022002020202020

220202020000202020

2000000000000000222222222222222 303003333 4040444404000044444444444444444444

BBBBBBBBBBBBBBB

CCCCCCCCCCCCCCCCCCCCCC

EEEEEEEEEEEEEEEE

111111

4444

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

AAACCCCCCCCCCCCCCCCCCCCC

DDDDDDDDDDDDDDDDDD

FFFFFFFFFFFFFFFF

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

29 Lesson 1-7

Finding Distance

Got It? On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform A and zip to each of the other platforms. How far do you travel from Platform D to Platform E? Each grid unit represents 5 m.

22. The equation is solved below. Write a justification for each step.

d 5 "(x2 2 x1)2 1 (y2 2 y1)2

DE 5 "(30 2 20)2 1 (215 2 20)2

5 "102 1 (235)2 5 "100 1 1225 5 "1325

23. To the nearest tenth, you travel about m.

Reasoning How does the Distance Formula ensure that the distance between two diff erent points is positive?

24. A radical symbol with no sign in front of it indicates a positive / negative square root.

25. Now answer the question.

__________________________________________________________________________________

Do you UNDERSTAND?


midpoint distance coordinate plane

Rate how well you can use the Midpoint and Distance Formulas.

Use the Distance Formula.

Sample: The radical in the Distance Formula represents a positive square root.

Substitute.

Simplify.

36.4

Answers may vary.


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Vocabulary

Review

Chapter 1 30

Perimeter, Circumference, and Area1-8

1. Cross out the shapes that are NOT polygons.

2. Write the name of each figure. Use each word once.

triangle square rectangle circle

Vocabulary Builder

consecutive (adjective) kun SEK yoo tiv

Definition: Consecutive means following in order without interruption.

Related Word: sequence

Example: The numbers 2, 4, 6, 8, . . . are consecutive even numbers.

Non-Example: The numbers 1, 3, 2, 5, 4, . . . are NOT consecutive numbers.

Use Your Vocabulary

Draw a line from each sequence of letters in Column A to the next consecutive letter in Column B.

Column A Column B

3. L, M, N, O, . . . R

4. V, U, T, S, . . . I

5. A, C, E, G. P

circle rectangle square triangle


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Problem 1

Problem 2

Key Concept Perimeter, Circumference, and Area

s

s

a c

b

hh

b

C r

d

24 m

c = dc = (24)c = 24

31 Lesson 1-8

Finding the Perimeter of a Rectangle

Got It? You want to frame a picture that is 5 in. by 7 in. with a 1-in.-wide frame. What is the perimeter of the picture?

7. The picture is in. by in.

8. Circle the formula that gives the perimeter of the picture.

P 5 4s P 5 2b 1 2h P 5 a 1 b 1 c C 5 pd

9. Solve using substitution.

10. The perimeter of the picture is in.

Finding Circumference

Got It? What is the circumference of a circle with radius 24 m in terms of ?

11. Error Analysis At the right is one students solution. What error did the student make?

_________________________________________________________

_________________________________________________________

12. Find the correct circumference.

6. Label the parts of each of the figures below.

Square Triangle Rectangle Circle

P 5 4s P 5 a 1 b 1 c P 5 2b 1 2h C 5 pd or C 5 2pr

A 5 s2 A 5 12bh A 5 bh A 5 pr2

5 7

24

P 5 2b 1 2h 5 2(5) 1 2(7) 5 10 1 14 5 24

C 5 2pr 5 2p(24) 5 48p

Answers may vary. Sample: The student used a diameter

of 24 m instead of a radius of 24 m.


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Problem 5

Problem 3

x

y

O 54321

2

3

4

5

12345

2

3

4

5

L

J

1M

K

7 ft

14 ft

Key Concept Postulate 110 Area Addition Postulate

Chapter 1 32

Finding Perimeter in the Coordinate Plane

Got It? Graph quadrilateral JKLM with vertices J(23, 23), K(1, 23), L(1, 4), and M(23, 1). What is the perimeter of JLKM?

13. Graph the quadrilateral on the coordinate plane at the right.

14. Use the justifications at the right to find the length of each side.

JK 5 P23 2 1 P Use the Ruler Postulate. 5 Simplify.

KL5 P 42 P Use the Ruler Postulate. 5 Simplify.

JM5 P 232 P Use the Ruler Postulate. 5 Simplify.

ML 5 (1 2 (23))2 1 (4 2 )2 Use the Distance Formula.

5 ( )

2 1 32 Simplify within parentheses.

5 ( ) 1 ( ) Simplify powers.

5 ( ) Add.

5 Take the square root.

15. Add the side lengths to find the perimeter.

JK 1 KL 1 JM 1 ML5 1 1 1 5

16. The perimeter of JKLM is units.

Finding Area of a Circle

Got It? The diameter of a circle is 14 ft. What is its area in terms of p?

17. Label the diameter and radius of the circle at the right.

18. Use the formula A 5 pr2 to find the area of the circle in terms of p.

19. The area of the circle is p ft2.

20. The area of a region is the sum / difference of the areas of its nonoverlapping parts.

4

4

4 4

16

25

20

20

5

49

5

9

4

7

7

1

1

23

A 5 pr2

5 p(7)2

5 49p


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Lesson Check

Now Iget it!

Need toreview

0 2 4 6 8 10

Math Success

Problem 6

9 cm

3 cm

3 cm

3 cm

6 cm

A1

A2

A3

3 cm

3 cm

9 cm

3 cm

9 cm

A1

A2A3

3 cm

9 cm A1 A1

A1

33 Lesson 1-8

Do you UNDERSTAND?

Compare and Contrast Your friend cant remember whether 2pr computes the circumference or the area of a circle. How would you help your friend? Explain.

22. Underline the correct word(s) to complete each sentence.

Area involves units / square units .

Circumference involves units / square units .

The formula 2pr relates to area / circumference because it involves units / square units .


perimeter area

Rate how well you can fi nd the area of irregular shapes.

Finding Area of an Irregular Shape

Got It? Reasoning The figure below shows one way to separate the figure at the left. What is another way to separate the figure?

21. Draw segments to show two different ways to separate the figure. Separate the left-hand figure into three squares. Drawings will vary. Samples are given.


002_HSM12_GEMCCH01_WR_013318594X003_HSM12_GEMCCH01_WR_013318594X004_HSM12_GEMCCH01_WR_013318594X005_HSM12_GEMCCH01_WR_013318594X006_HSM12_GEMCCH01_WR_013318594X007_HSM12_GEMCCH01_WR_013318594X008_HSM12_GEMCCH01_WR_013318594X009_HSM12_GEMCCH01_WR_013318594X010_HSM12_GEMCCH01_WR_013318594X011_HSM12_GEMCCH01_WR_013318594X012_HSM12_GEMCCH01_WR_013318594X013_HSM12_GEMCCH01_WR_013318594X014_HSM12_GEMCCH01_WR_013318594X015_HSM12_GEMCCH01_WR_013318594X016_HSM12_GEMCCH01_WR_013318594X017_HSM12_GEMCCH01_WR_013318594X018_HSM12_GEMCCH01_WR_013318594X019_HSM12_GEMCCH01_WR_013318594X020_HSM12_GEMCCH01_WR_013318594X021_HSM12_GEMCCH01_WR_013318594X022_HSM12_GEMCCH01_WR_013318594X023_HSM12_GEMCCH01_WR_013318594X024_HSM12_GEMCCH01_WR_013318594X025_HSM12_GEMCCH01_WR_013318594X026_HSM12_GEMCCH01_WR_013318594X027_HSM12_GEMCCH01_WR_013318594X028_HSM12_GEMCCH01_WR_013318594X029_HSM12_GEMCCH01_WR_013318594X030_HSM12_GEMCCH01_WR_013318594X031_HSM12_GEMCCH01_WR_013318594X032_HSM12_GEMCCH01_WR_013318594X033_HSM12_GEMCCH01_WR_013318594X

Documents

1-1 Nets and Drawings for Visualizing Geometrymrroosmustangmath.weebly.com/uploads/3/1/7/3/31739055/chapter_1... · Visualizing Geometry 1-1 ... Triangles, rectangles, pentagons,