Chapter 6 Practice Test #1 - M2 Mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/52631585/chapter_6... · Chapter 6 Practice Test #1 Class Name : M29 Geometry - 2019-20 Term1 Instructor

Chapter 6 Practice Test #1

Class Name : M29 Geometry - 2019-20 Term1 Instructor Name : Mr. Beckey

Student Name : _____________________ Instructor Note :

1. A rectangular field is meters long and meters wide.

Give the length and width of another rectangular field that has the same perimeter but a smaller area.

width meters

length meters

2. Choose the term that has the given definition.

Term Definition

{Angle, Circle, Perpendicular lines, Parallel lines, Linesegment, Congruent, Collinear, Coplanar}

Belonging to the same plane

{Angle,Circle,Perpendicular lines,Parallel lines,Linesegment,Congruent,Collinear,Coplanar}

The set of all points in a plane that lie the same distance from a singlepoint in the plane


Belonging to the same line


A part of a line consisting of two endpoints and all points between them

3. Find the length of the toothpick.

110 75

= =

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 6 Pr ac t i ce T es t #1 Page 1 / 18

3. Find the length of the toothpick.

Write your answer to the nearest centimeter.

4. The figure below has a point marked with a large dot.

First, translate the figure units to the right and units up.Then, give the coordinates of the marked point in the original figure and the final figure.

Point in original figure:Point in final figure:

5. Find the perimeter of the square. Be sure to write the correct unit in your answer.

5 6

cm

0 1 2 3 4 5 6 7 8 9 10 11 12

xx

-1-2-3-4-5-6-7-8 1 2 3 4 5 6 7 8

yy

-1-2-3-4-5-6-7-8

12345678


5. Find the perimeter of the square. Be sure to write the correct unit in your answer.

6. Consider parallelogram below.

Use the information given in the figure to find , , and .

7. Use the given information to complete the proof of the following theorem.

EFGH

x m∠ IHE m∠ IEH

16 m

47°

33°

7

−3x 2I

E

F

G

H



If opposite sides of a quadrilateral are congruent, then it is a parallelogram.

By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.Use this definition in your proof.

Given:

Prove: is a parallelogram


=~QR ST=~QT RS

QRST

Statement Reason

1 =~QR ST Given

2 =~QT R S Given

3 =~ Reflexive Property

4 =~ _______________

5 =~∠ 1 ∠ CPCTC Property 4

6 =~∠ 2 ∠ CPCTC Property 4

7 QR _______________

8 QT _______________

9 QR ST is a parallelogram _______________

Line(s) Used

T

4

Q

1

R2

S

3



If a quadrilateral is a parallelogram, then its opposite angles are congruent.

By definition, a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.Use this definition in your proof.

Given: is a parallelogram

Prove:

9. Three vertices of a parallelogram are shown in the figure below.Give the coordinates of the fourth vertex.

QRST

=~∠ R ∠ T=~∠ Q ∠ S

Statement Reason

1 QR ST is a parallelogram Given

2 QR Definition of a Parallelogram 1

3 ∠ and ∠ T are supp. angles _______________

4 ∠ and ∠ S are supp. angles _______________

5 QT Definition of a Parallelogram 1

6 ∠ and ∠R are supp. angles _______________

7 =~∠R ∠ If s are supp. to the same , they are ∠ ∠ =~ 3 6

8 =~∠Q ∠ If s are supp. to the same , they are ∠ ∠ =~ 4 6

Line(s) Used

TQ

R S

xx

yy

, , 22 55

, , −− 55 00

, , −− 11 −− 33


10. Consider quadrilateral below.

Note that has vertices , , , and .

Complete the following to determine if is a parallelogram.

WXYZ

WXYZ W , 2 − 8 X , 6 − 1 Y , 3 1 Z , −1 − 6WXYZ

(a) Find the length of and the length of .Give exact answers (not decimal approximations).

WZ XY

Length of :WZ

Length of :XY

(b) Find the slope of and the slope of .WZ XY

Slope of :WZ

Slope of :XY

(c) From parts (a) and (b), what can we conclude?

The quadrilateral is a parallelogram because it has one pair of opposite sides that are bothcongruent and parallel.

The quadrilateral is a parallelogram because it has one pair of opposite sides that arecongruent, even though those sides are not parallel.

The quadrilateral is a parallelogram because it has one pair of opposite sides that areparallel, even though those sides are not congruent.

The quadrilateral is not a parallelogram.

It cannot be determined if the quadrilateral is a parallelogram.

xx

-1-2-3-4-5-6-7-8-9 1 2 3 4 5 6 7 8 9

yy

-1-2-3-4-5-6-7-8-9

123456789

W

X

Y

Z


11. Given the information marked on the figures below, classify each quadrilateral as a "Parallelogram" or "Notnecessarily a parallelogram."

Note that each figure is drawn like a parallelogram, but you should not rely on how the figure is drawn in determiningyour answers.

___ Parallelogram___ Not necessarily a parallelogram




12. In the rectangle below, = +4 6 = +5 1 =∠ 32 °

V W

YX

K L

NM

R

S U

T

A

B D

C


12. In the rectangle below, , , and .

Find and .

13. Given the information marked on each figure below, select all classifications that must be true.

Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determiningyour answers.

___ Quadrilateral___ Parallelogram___ Rectangle



14. Consider parallelogram below.

=JN +4x 6 =KN +5x 1 =m∠ NML 32 °JL m∠ NJM

PQRS

JJ KK

LLMM

NN

A

B

C

D

R

S

T

U

P Q

R S


Note that has vertices , , , and .Answer the following to determine if the parallelogram is a rectangle, rhombus, square, or none of these.

PQRS P −−1, 5 Q −4, 2 R 1, 3 S −4, 4

(a) Find the slope of and the slope of a side adjacent to .RS RS

Slope of :RS

Slope of side adjacent to :RS

(b) Find the length of and the length of a side adjacent to .Give exact answers (not decimal approximations).

RS RS

Length of :RS

Length of side adjacent to :RS

(c) From parts (a) and (b), what can we conclude about parallelogram

? Check all that apply.PQRS

is a rectangle.PQRS

is a rhombus.PQRS

is a square.PQRS

is none of these.PQRS

xx

-2-4-6-8 2 4 6 8

yy

-2

-4

-6

-8

2

4

6

8

P

Q

R

S


15. For the rhombus below, find the measures of , , , and .

_____

_____

_____

_____

16. shape:parallelogram -- shape:rectangle -- shape:square

∠ 1 ∠ 2 ∠ 3 ∠ 4

=m∠ 1 °=m∠ 2 °=m∠ 3 °=m∠ 4 °

4242 °°

11

22

3344


Answer the questions about the figures below.

Figure A

Figure B

Figure C

17. For each of the following quadrilaterals, select all the properties that must be true.

(a) Which figures are rectangles?Mark all that apply.

Figure A Figure B Figure C None of the figures

(b) Which figures are parallelograms?Mark all that apply.


(c) Which figures are squares?Mark all that apply.


2 in

3 in

2 in

3 in

2 in

3 in

2 in

3 in

3 in

3 in

3 in

3 in


17. For each of the following quadrilaterals, select all the properties that must be true.

18. True or False?

a. Every quadrilateral is a square.

b. Every parallelogram is a rectangle.

c. Every rectangle is a rhombus.

d. Every rhombus with four right angles is a square.

Two pairs of parallelsides

Only one pair ofparallel sides

Four right angles All sides congruent

Parallelogram

Trapezoid

Square


Chapter 6 Practice Test #1 Answers for class M29 Geometry -2019-20 Term1

1.

width meters

length meters

2.

3. centimeters

4.

= 65= 120

Term Definition

Coplanar Belonging to the same plane

Circle The set of all points in a plane that lie the same distance from asingle point in the plane

Collinear Belonging to the same line

Line segmentA part of a line consisting of two endpoints and all points betweenthem

8


4.

Point in original figure:

Point in final figure:

5.

6.

7.

, −4 −8, 1 −2

64 m

=x 3=m∠ IHE 33 °=m∠ IEH 47 °

xx

-1-2-3-4-5-6-7-8 1 2 3 4 5 6 7 8

yy

-1-2-3-4-5-6-7-8

12345678


7.

8.

9.

10.

Statement Reason

1 =~QR ST Given

2 =~QT R S Given

3 =~R T R T Reflexive Property

4 =~QRT STR SSS Congruence Property 1 2 3

5 =~∠ 1 ∠ 4 CPCTC Property 4

6 =~∠ 2 ∠ 3 CPCTC Property 4

7 QR ST If alt. int. s , then lines ∠ =~ 5

8 QT R S If alt. int. s , then lines ∠ =~ 6

9 QR ST is a parallelogram Definition of a Parallelogram 7 8

Line(s) Used

Statement Reason

1 QR ST is a parallelogram Given

2 QR ST Definition of a Parallelogram 1

3 ∠Q and ∠ T are supp. angles If lines , then cons. int. s are supp.∠ 2

4 ∠R and ∠ S are supp. angles If lines , then cons. int. s are supp.∠ 2

5 QT R S Definition of a Parallelogram 1

6 ∠Q and ∠R are supp. angles If lines , then cons. int. s are supp.∠ 5

7 =~∠R ∠ T If s are supp. to the same , they are ∠ ∠ =~ 3 6

8 =~∠Q ∠ S If s are supp. to the same , they are ∠ ∠ =~ 4 6

Line(s) Used

, −2 8


10.

11.

(a) Find the length of and the length of .Give exact answers (not decimal approximations).

WZ XY

Length of :WZ 13

Length of :XY 13

(b) Find the slope of and the slope of .WZ XY

Slope of :WZ −2

3

Slope of :XY −2

3

(c) From parts (a) and (b), what can we conclude?

The quadrilateral is a parallelogram because it has one pair of opposite sides that are bothcongruent and parallel.

The quadrilateral is a parallelogram because it has one pair of opposite sides that arecongruent, even though those sides are not parallel.

The quadrilateral is a parallelogram because it has one pair of opposite sides that areparallel, even though those sides are not congruent.

The quadrilateral is not a parallelogram.

It cannot be determined if the quadrilateral is a parallelogram.


11.

___ Not necessarily a parallelogram

___ Not necessarily a parallelogram

___ Parallelogram

___ Parallelogram

12.

13.

JL = 52

m∠ NJM = 58 °

V W

YX

K L

NM

R

S U

T

A

B D

C


13.

14.

15.

(a)

A

B

C

D (b)

R

S

T

U (c)P Q

R S

Quadrilateral Quadrilateral Quadrilateral

Parallelogram Parallelogram Parallelogram

Rectangle Rectangle Rectangle

(a) Find the slope of and the slope of a side adjacent to .RS RS

Slope of :RS −7

3

Slope of side adjacent to :RS1

5

(b) Find the length of and the length of a side adjacent to .Give exact answers (not decimal approximations).

RS RS

Length of :RS 58

Length of side adjacent to :RS 26

(c) From parts (a) and (b), what can we conclude about parallelogram

? Check all that apply.PQRS

is a rectangle.PQRS

is a rhombus.PQRS

is a square.PQRS

is none of these.PQRS

=∠ 1 42 ° © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 6 Pr ac t i ce T es t #1 Page 18 / 18

15.

16.

17.

18.

a. Every quadrilateral is a square.False

b. Every parallelogram is a rectangle.False

c. Every rectangle is a rhombus.False

d. Every rhombus with four right angles is a square.True

=m∠ 1 42 °=m∠ 2 48 °=m∠ 3 48 °=m∠ 4 48 °

(a) Which figures are rectangles?Mark all that apply.


(b) Which figures are parallelograms?Mark all that apply.


(c) Which figures are squares?Mark all that apply.


Two pairs of parallelsides

Only one pair ofparallel sides

Four right angles All sides congruent

Parallelogram

Trapezoid

Square

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Chapter 6 Practice Test #1 - M2 Mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/52631585/chapter_6... · Chapter 6 Practice Test #1 Class Name : M29 Geometry - 2019-20 Term1 Instructor