Course 3 • Chapter 7 Congruence and Similarity 165

NAME _____________________________________________ DATE __________________ PERIOD _________

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Test, Form 3A

1.

2.

3.

4.

5.

6a.

6b.

1. The floors of houses in Japan are traditionally covered by tatami. Tatami are rectangular-shaped straw mats that measure about 6 feet by 3 feet. If a room is 48 feet by 24 feet, how many tatami are needed to cover the floor? Use the draw a diagram strategy.

2. Determine whether the pair of polygons

8

611

4

3 5.5is similar using properties of similar polygons. Explain your reasoning.

3. A road sign casts a shadow that is 4 feet long. At the same time, a 6-foot man standing next to the sign casts a shadow that is 2.4 feet long. How tall is the sign?

4. The length of a rectangle is 22 centimeters and the width is 4 centimeters. A similar rectangle has a width of 6 centimeters. What is the perimeter of the second rectangle?

5. Determine whether the triangles are similar. If so, write a similarity statement.

50°75°

55°75°

M O

Q

P

N

L

6. The triangles below are congruent.

C

A

F

GH

B

a. Write congruency statements comparing the corresponding parts.

b. Describe a series of transformations that maps �ABC onto �FGH.

64 tatami

similar; The corresponding angles are congruent and the corresponding sides are proportional.

10 ft

78 cm

similar;

�LMN ˜ �OPQ

∠A � ∠F;

∠B � ∠G;

∠C � ∠H; −−

AB � −−

FG ; −−

BC � −−

GH ; −−

AC � −−

FH

Sample answer:

reflection then

translation

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Course 3 • Chapter 7 Congruence and Similarity 166

NAME _____________________________________________ DATE __________________ PERIOD _________

SCORE _________Copyright ©

The McG

raw-H

ill Companies, Inc. Perm

ission is granted to reproduce for classroom use.

7. Triangle GHJ has vertices at (0, 1), (4, 0), and (4, 1).

a. Graph �GHJ.

b. Reflect �GHJ over the y-axis, then translate it 3 units up. Label the vertices of the image G′H′J′.

c. Are the two triangles congruent? Justify your response.

8. Determine if the two figures are similar by using transformations. Explain your reasoning.

xO

y

J K

LM

A B

CD

9. Use the similar slope triangles to show that the slope of the line is the same between any two distinct points on the line.

xO

y

A

BCF

GH

10. Two rectangles are similar. The length and width of the first rectangle is 8 meters by 6 meters. The second rectangle is similar by a scale factor 5. What is the area of the second rectangle?

Test, Form 3A (continued)

7a, b.

7c.

8.

9.

10.

xO

y

1 2 3 4

34

21

-3-2

-4

-3-2-4

yes; A reflection

followed by a

translation will

map �GHJ onto

�G′H′J′.

not similar; The

ratios comparing

the corresponding

side lengths are

not equal so a

dilation did not

occur.

Sample answer:

AB

−− BC

= -2

−− 2 = -1

and

FG

−− GH

= -4

−− 4 = - 1

1,200 m2

JH

G

G′

J′

H′

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P rinter P DF