chapter 3 practice test #1 -...

Chapter 3 Practice Test #1

Statement about reflected figures True False

If two sides are parallel in the original figure,then those sides may not be parallel in thefinal figure.

The final side lengths are the same as theoriginal side lengths.

The final angle measures are smaller thanthe original angle measures.

The original figure and the final figure maynot be congruent.

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

Student Name : _____________________ Instructor Note :

1. Reflect the figure across the -axis. Then decide if each statement about reflected figures is true or false.

2. Reflecting across the vertical line

, we get its image

.

Suppose , ,

and intersect the

line of reflection at ,

, and as shownbelow.

Complete the following.

(a) Select all that apply.

is parallel to , and is perpendicular to .

, , and are each parallel to the line of reflection.

, , and are each perpendicular to the line of reflection.None of the above

(b) Suppose each pair of segments below have the same length.

___ units

___ units

___ units

(c) Choose the correct statement about the reflection.

The line of reflection is parallel to each side of the original and final figures.

x

DEF

=x 2D 'E 'F '

DD ' EE 'FF '

J

K L

DD ' EE ' DD ' FF 'DD ' EE ' FF 'DD ' EE ' FF '

=DJ =D 'J=EK =E 'K=FL =F 'L

xx

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

yy

-2

-4

-6

-8

2

4

6

8

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10

DD

EE

FF

DD ''

EE ''

FF ''

JJ

KK

LL

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 3 Pr ac t i ce T es t #1 / 30

The line of reflection is the perpendicular bisector of each segment joining a point and its image.The line of reflection is neither parallel nor perpendicular to each segment joining a point and its image.The line of reflection is parallel to each segment joining a point and its image.

3. In each part, reflect the solid figure exactly onto the dashed figure.

(a) (b)

4. Draw the reflection of the following triangle over the line .

5. Draw the reflection of the triangle across the .

n

x

xx

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

yy

-2

-4

-6

-8

2

4

6

8

xx

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

yy

-2

-4

-6

-8

2

4

6

8

xx

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

yy

-2

-4

-6

-8

2

4

6

8 n


5. Draw the reflection of the triangle across the -axis.

6. Triangle is reflected across the

x

TRS x

xx

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

yy

-2

-4

-6

-8

2

4

6

8


6. Triangle is reflected across the -axis.

The result is , as shown below.

(a) The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give thecoordinates after the reflection.

original coordinates final coordinates

_____, _____

_____, _____

_____, _____

(b) Choose the general rule below that describes the reflection mapping to .

7. Translate the figure units to the right. Then decide if each statement about translated figures is true or false.

TRS x

T 'R 'S '

→T , −6 5 → T 'R , 4 7 → R 'S , −3 2 → S '

TRS T 'R 'S '

, x y → , x −y , x y → , y x, x y → , −x y , x y → , −x −y, x y → , −y x , x y → , −y −x, x y → , y −x

4

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10

T

R

S

T '

R '

S '



Statement about translated figures True False

The final angle measures are the same as theoriginal angle measures.

The final side lengths are shorter than theoriginal side lengths.

The original figure and the final figure may notbe congruent.

If two sides are parallel in the original figure,then those sides may not be parallel in the finalfigure.

8. Translating to the right units and downward unit, we get its image

4

FGH 6 1 F 'G 'H '

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


8. Translating to the right units and downward unit, we get its image .

Note that has vertices , , and .

Also, note that has vertices , , and .Complete the following.

(a) Find each length. Give exact answers (not decimal approximations).

___ units

___ units

___ units

(b) Find each slope. Give exact answers (not decimal approximations).

Slope of ___

Slope of ___

Slope of ___

(c) Choose the correct statement about the translation.

All points on the original figure moved the same distance and in the same direction.All points on the original figure moved in the same direction, but not all points moved the same distance.All points on the original figure moved the same distance, but not all points moved in the same direction.The points on the original figure didn't all move the same distance and didn't all move in the same direction.

9. In each part, translate the solid figure exactly onto the dashed figure.

FGH 6 1 F 'G 'H '

FGH F , −3 8 G , −2 3 H , −7 2F 'G 'H ' F ' , 3 7 G ' , 4 2 H ' , −1 1

=FF '=GG '=HH '

=FF '=GG '=HH '

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10

FF

GGHH

FF ''

GG ''HH ''


9. In each part, translate the solid figure exactly onto the dashed figure.

If this is not possible, click on "Not possible".

(a) (b)

10. Draw the following triangle after a translation unit to the right and units down.

11. Triangle is translated units to the right and units up.

1 4

DEF 8 7

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

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

xx

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

yy

-2

-4

-6

-8

2

4

6

8


11. Triangle is translated units to the right and units up.


(a) The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks togive the coordinates after the translation.

(b) Choose the general rule below that describes the translation mapping to .

12. Rotate the figure clockwise about the origin. Then decide if each statement about rotated figures is true or false.

DEF 8 7D 'E 'F '

→D , −8 − 1 D ' , →E , −4 − 5 E ' , →F , −7 − 4 F ' ,

DEF D 'E 'F '

→, x y , 7x 8y →, x y , +x 8 + y 7→, x y , 8x 7y →, x y , −7x − 8y→, x y , −8x − 7y →, x y , −x 8 − y 7→, x y , +x 7 + y 8 →, x y , −x 7 − y 8

90°

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

12

34

56

78

9

D

EF

D '

E 'F '



Statement about rotated figures True False

The final side lengths are longer than the original sidelengths.

The final angle measures are larger than the original anglemeasures.

The original figure and the final figure are congruent.

If two sides are parallel in the original figure, then thosesides may not be parallel in the final figure.

13. Rotating by counterclockwise about the origin, we get its image as shown below.

90°

ABK 90° A 'B 'K '

xx

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

yy

-2

-4

-6

-8

2

4

6

8


13. Rotating by counterclockwise about the origin, we get its image as shown below.

Note that has vertices , , and .

Also, note that has vertices , , and .Complete the following.

(a) Suppose each pair of segments below have the same length.Find each length. Give exact answers (not decimal approximations).

___ units

___ units

___ units

(b) Suppose the angles below have the same measure. Choose the correct angle measure. Use a protractor, as necessary.

{ , , , , , }

(c) Choose the correct pair of statements about the rotation.

Not every point on the original figure is the same distance from the center of rotation as its image.Not all angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

Each point on the original figure is the same distance from the center of rotation as its image.Not all angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

Not every point on the original figure is the same distance from the center of rotation as its image.All angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

Each point on the original figure is the same distance from the center of rotation as its image.All angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

14. In each part, rotate the solid figure about the origin exactly onto the dashed figure.

ABK 90° A 'B 'K 'ABK A , −5 8 B , −6 4 K , −8 3A 'B 'K ' A ' , −8 −5 B ' , −4 −6 K ' , −3 −8

=CA =CA '=CB =CB '=CK =CK '

=m∠ACA ' =m∠BCB ' =m∠KCK ' 30° 60° 90° 120° 150° 180°

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10

C

AA

AA ''

BB

BB ''

KK

KK ''


14. In each part, rotate the solid figure about the origin exactly onto the dashed figure.


(a)

(b)

15. Draw the following triangle after a clockwise rotation about the origin. 90°

xx

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

yy

-2

-4

-6

-8

2

4

6

8

xx

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

yy

-2

-4

-6

-8

2

4

6

8


15. Draw the following triangle after a clockwise rotation about the origin.

16. A regular hexagon is shown below. Suppose that the hexagon is rotated clockwise about its center so that the vertex at is moved

to . How many degrees does the hexagon rotate?

17. Triangle is rotated counterclockwise about the origin.

90°

N

J

RST 90°

xx

-2-4-6 2 4 6

yy

-2

-4

-6

2

4

6

JJKK

LL

MM NN

OO


17. Triangle is rotated counterclockwise about the origin.


(a) The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give thecoordinates after the rotation.


_____, _____

_____, _____

_____, _____

(b) Choose the general rule below that describes the rotation mapping to .

18. Reflect over the

RST 90°R 'S 'T '

→R , −1 3 → R 'S , 2 6 → S 'T , 8 4 → T '

RS T R 'S 'T '

, x y → , −x −y , x y → , y x, x y → , −x y , x y → , −y x, x y → , −y −x , x y → , x −y, x y → , y −x

, 4 − 4 y

xx

-2-4-6-8-10 2 4 6 8 10

yy

-2

-4

-6

-8

-10

2

4

6

8

10

R

S

T

R '

S '

T '


18. Reflect over the -axis.

Then translate the result to the right units.

What are the coordinates of the final point?

___, &sp;___

19. Answer the questions about Figure A and Figure B below.

, 4 − 4 y

3

xx

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

yy

-2

-4

-6

-8

2

4

6

8


19. Answer the questions about Figure A and Figure B below.

(a) Are Figure A and Figure B congruent?

Yes No

(b) Which sequence(s) of transformations will map Figure A onto Figure B exactly? Choose all that apply.

Translate Figure A to the left units, and then rotate that result clockwise about the origin.

Reflect Figure A over the -axis, and then rotate that result counterclockwise about the origin.

Rotate Figure A counterclockwise about the origin, and then translate that result down units.

Rotate Figure A counterclockwise about the origin, and then reflect that result over the -axis.

None of these

20. Answer each question below.

7 180°

y 90°

90° 7

90° x

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

Figure A

Figure B


20. Answer each question below.

Are Figure A and Figure B congruent? Yes No

Which transformation will map Figure A ontoFigure B exactly?

Translate Figure A to the left units

Translate Figure A down units

Reflect Figure A over the -axis


Rotate Figure A clockwise about theorigin

Rotate Figure A counterclockwise about the origin

None of these

Are Figure C and Figure D congruent? Yes No

Which transformation will map Figure C ontoFigure D exactly?

Translate Figure C to the right units

Translate Figure C up units

Reflect Figure C over the -axis


Rotate Figure C clockwise about theorigin

Rotate Figure C counterclockwise about the origin

None of these

21. In each part, use the tools to move the solid triangle exactly onto the dashed triangle.

66x

y

90°

180°

44x

y

180°

90°

xx

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

yy

-2

-4

-6

-8

2

4

6

8Figure A

Figure B

xx

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

yy

-2

-4

-6

-8

2

4

6

8

Figure C Figure D


21. In each part, use the tools to move the solid triangle exactly onto the dashed triangle.


(a)

(b)

22. Draw all lines of symmetry for the following figure.

23. For each figure below, determine if it has rotational symmetry.© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 3 Pr ac t i ce T es t #1 / 30

23. For each figure below, determine if it has rotational symmetry.If it does, give the smallest angle of rotation needed for the figure to appear unmoved.

Rotational symmetry? __ Yes __ No

Angle? ____

Rotational symmetry? __ Yes __ No

Angle? ____

24. A rectangle is shown below.© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.C hapter 3 Pr ac t i ce T es t #1 / 30

24. A rectangle is shown below.

Line intersects two vertices.

Line bisects each side it passes through.

Point is the center of the rectangle.

25. A regular hexagon is shown below.

m

n

X

Which transformation(s) must map the rectangle exactly ontoitself? Choose all that apply.

Clockwise rotation about by X 90°Reflection across line m

Reflection across line n

Counterclockwise rotation about by X 180°None of the above

X

mn


25. A regular hexagon is shown below.

Line passes through a vertex and bisects a side.

Line passes through two vertices.

Point is the center of the hexagon.

a

b

P

Which transformation(s) must map the hexagon exactly ontoitself? Choose all that apply.

Reflection across line b

Counterclockwise rotation about by P 60°

Clockwise rotation about by P 180°

Reflection across line a

None of the above

P

a

b


Chapter 3 Practice Test #1 Answers for class M29 Geometry - 2019-20Term1

1. Reflect the figure across the -axis. Then decide if each statement about reflected figures is true or false.

Statement about reflected figures True False


The final side lengths are the same as the original sidelengths.

The final angle measures are smaller than the originalangle measures.

The original figure and the final figure may not becongruent.

2. (a) Select all that apply.

is parallel to , and is perpendicular to .

, , and are each parallel to the line of reflection.

, , and are each perpendicular to the line of reflection.None of the above

(b) Suppose each pair of segments below have the same length.

units

units

units

(c) Choose the correct statement about the reflection.

The line of reflection is parallel to each side of the original and final figures.The line of reflection is the perpendicular bisector of each segment joining a point and its image.The line of reflection is neither parallel nor perpendicular to each segment joining a point and its image.The line of reflection is parallel to each segment joining a point and its image.

3.

x

DD ' EE ' DD ' FF 'DD ' EE ' FF 'DD ' EE ' FF '

=DJ =D 'J 4=EK =E 'K 5=FL =F 'L 3

xx

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

yy

-2

-4

-6

-8

2

4

6

8


3.

4.

5.

6.

xx

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

yy

-2

-4

-6

-8

2

4

6

8

Not possible

xx

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

yy

-2

-4

-6

-8

2

4

6

8 n

xx

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

yy

-2

-4

-6

-8

2

4

6

8


6.

(a) The arrows below show that the coordinates on the left are mappedto the coordinates on the right. Fill in the blanks to give thecoordinates after the reflection.


(b) Choose the general rule below that describes the reflection mapping to .


Statement about translated figures True False

The final angle measures are the same as the originalangle measures.

The final side lengths are shorter than the original sidelengths.

The original figure and the final figure may not becongruent.


8.

→T , −6 5 → T ' , −6 −5R , 4 7 → R ' , 4 −7S , −3 2 → S ' , −3 −2

TRS T 'R 'S '

, x y → , x −y , x y → , y x, x y → , −x y , x y → , −x −y, x y → , −y x , x y → , −y −x, x y → , y −x

4

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


8. (a) Find each length. Give exact answers (not decimal approximations).

units

units

units

(b) Find each slope. Give exact answers (not decimal approximations).

Slope of

Slope of

Slope of

(c) Choose the correct statement about the translation.

All points on the original figure moved the same distance and in the same direction.All points on the original figure moved in the same direction, but not all points moved the same distance.All points on the original figure moved the same distance, but not all points moved in the same direction.The points on the original figure didn't all move the same distance and didn't all move in the same direction.

9.

(a) (b)

10.

11.

=FF ' 37=GG ' 37=HH ' 37

=FF ' −16

=GG ' −16

=HH ' −16

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

Not possible

xx

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

yy

-2

-4

-6

-8

2

4

6

8


11. (a) The arrows below show that the coordinates on the left are mapped to the coordinates on the right. Fill in the blanks to give the

coordinates after the translation.

(b) Choose the general rule below that describes the translation mapping to .


Statement about rotated figures True False

The final side lengths are longer than the original sidelengths.

The final angle measures are larger than the original anglemeasures.

The original figure and the final figure are congruent.


13. (a) Suppose each pair of segments below have the same length.

Find each length. Give exact answers (not decimal approximations).

units

units

units

(b) Suppose the angles below have the same measure. Choose the correct angle measure. Use a protractor, as necessary.

(c) Choose the correct pair of statements about the rotation.

Not every point on the original figure is the same distance from the center of rotation as its image.Not all angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

Each point on the original figure is the same distance from the center of rotation as its image.Not all angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

Not every point on the original figure is the same distance from the center of rotation as its image.All angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

Each point on the original figure is the same distance from the center of rotation as its image.All angles formed by a point and its image, with the vertex at the center of rotation, are congruent.

14.

→D , −8 − 1 D ' , 0 6→E , −4 − 5 E ' , 4 4→F , −7 − 4 F ' , 1 1

DEF D 'E 'F '

→, x y , 7x 8y →, x y , +x 8 + y 7→, x y , 8x 7y →, x y , −7x − 8y→, x y , −8x − 7y →, x y , −x 8 − y 7→, x y , +x 7 + y 8 →, x y , −x 7 − y 8

90°

=CA =CA ' 89=CB =CB ' 52=CK =CK ' 73

=m∠ACA ' =m∠BCB ' =m∠KCK ' 90°

xx

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

yy

-2

-4

-6

-8

2

4

6

8


14.

(a)

(b)

15.

16. 120°

Not possible

xx

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

yy

-2

-4

-6

-8

2

4

6

8

xx

-2-4-6 2 4 6

yy

-2

-4

-6

2

4

6

, − 4 − 1, − 1 − 2

, − 3 − 5


16.

17.

(a) The arrows below show that the coordinates on the left are mappedto the coordinates on the right. Fill in the blanks to give thecoordinates after the rotation.


(b) Choose the general rule below that describes the rotation mapping to .

18.

19. (a) Are Figure A and Figure B congruent?

Yes No

(b) Which sequence(s) of transformations will map Figure A onto Figure B exactly? Choose all that apply.

Translate Figure A to the left units, and then rotate that result clockwise about the origin.

Reflect Figure A over the -axis, and then rotate that result counterclockwise about the origin.

Rotate Figure A counterclockwise about the origin, and then translate that result down units.

Rotate Figure A counterclockwise about the origin, and then reflect that result over the -axis.

None of these

20.

120°

→R , −1 3 → R ' , −3 −1S , 2 6 → S ' , −6 2T , 8 4 → T ' , −4 8

RS T R 'S 'T '

, x y → , −x −y , x y → , y x, x y → , −x y , x y → , −y x, x y → , −y −x , x y → , x −y, x y → , y −x

, −1 − 4

7 180°

y 90°

90° 7

90° x


20.

Are Figure A and Figure B congruent? Yes No

Which transformation will map Figure A ontoFigure B exactly?

Translate Figure A to the left units

Translate Figure A down units



Rotate Figure A clockwise about theorigin

Rotate Figure A counterclockwise about the origin

None of these

Are Figure C and Figure D congruent? Yes No

Which transformation will map Figure C ontoFigure D exactly?

Translate Figure C to the right units

Translate Figure C up units



Rotate Figure C clockwise about theorigin

Rotate Figure C counterclockwise about the origin

None of these

21.

66x

y

90°

180°

44x

y

180°

90°

xx

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

yy

-2

-4

-6

-8

2

4

6

8Figure A

Figure B

xx

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

yy

-2

-4

-6

-8

2

4

6

8

Figure C Figure D


21.

(a)

(b)

22.

23.

Not possible


23.

24.

25.

Rotational symmetry? Yes No Rotational symmetry? Yes No

Angle? 45 ° Angle? °

Which transformation(s) must map the rectangle exactly ontoitself? Choose all that apply.

Clockwise rotation about by X 90°Reflection across line m

Reflection across line n

Counterclockwise rotation about by X 180°None of the above

Which transformation(s) must map the hexagon exactly ontoitself? Choose all that apply.

Reflection across line b

Counterclockwise rotation about by P 60°

Clockwise rotation about by P 180°

Reflection across line a

None of the above


chapter 3 practice test #1 -...

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