Course 3 Chapter 2 Similarity and Dilations 19

Program: M. S. Math 2013

Vendor: Six Red Marbles

Component: C02_CT

Grade: Course 3Press PDF

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.Chapter 2 Test, Form 3AEach pair of polygons is similar. Determine the missing side measures. 8.3(A)

1. ABC XYZ

4 in.7 in.

5.25 in.3 in.6 in.

A

B

CZ

X

Y

2.

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?

8.3(A)

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?

8.3(A)

5. Determine whether the triangles are similar by angle-angle similarity. If so, write a similarity statement. 8.8(D)

6. In the figure, triangle ABC is similar to triangle DEC. Determine the distance from point D to point E. 8.3(A)

7. A telephone pole casts a shadow that is 20 feet long. At the same time, a 5-foot-tall woman standing on a 1.5-foot-tall podium next to the telephone pole casts a shadow that is 15 feet long. How tall is the telephone pole? 8.3(A)

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

second rectangle? 8.3(A)

2 mm? mm

6 mm

10 mm

15 mm

5 mm

5075

5575

M R

Q

P

N

L

60 yd

90 yd

180 ydd yd

E

CA

B

D

10.5 in. 4 mm

10 ft

78 cm

yes; L R and M P, so LMN RPQ

90 yd

8 2 _ 3 ft

1,200 m 2

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Course 3 Chapter 2 Similarity and Dilations20

Program: M. S. Math 2013

Vendor: Six Red Marbles

Component: C02_CT

Grade: Course 3Press PDF

NAME ___________________________________________________ DATE ______________________ PERIOD ____________

SCORE _____________Copyright

McG

raw-H

ill Education. Permission is granted to reproduce for classroom

use.Chapter 2 Test, Form 3A (continued) 9. A projector transforms the image on a computer screen so that it is dilated by a scale

factor of 7 _ 2 . The original image on the screen is 10 inches wide. Find the new width after it is projected on the wall. 8.3(A)

10. A magazine designer uses 6.5-inch by 8.5-inch paper to mock up an advertisement. The original advertisement appears in a box with dimensions 1.3 inches by a inches. Find the scale factor the designer used and the value of a. Explain. 8.3(A)

11. Triangle DEF has vertices D(2, 5), E(2, 7), and F(5, 5). The triangle is dilated with a scale factor of 1 _ 5 , and the dilation will be centered at the origin. Write an algebraic representation for the dilation. Determine the coordinates of the image of point F after the dilation. 8.3(B), 8.3(C)

Use a problem-solving model to solve each problem.

12. An E-shaped figure is formed by four rectangles having areas of 440square centimeters, 240 square centimeters, 240square centimeters, and 120 square centimeters. Jason dilates the figure by a scale factor of 1 _ 4 . What is the total area of the new E-shaped figure? 8.10(D)

13. Mark is painting two rectangular doors. Thefirst door has an area of 150 square feet. Thesecond door is a dilation of first door witha scale factor of 1.4. One gallon of paint will cover 80 square feet. How many gallons ofpaint will Mark use to paint both doors?

8.10(D)

14. Polygon ABCD has vertices A(5, -2) B(3, -2), C(3, 3), and D(5, 3). Polygon ABCD is dilated using the origin as the center of the dilation. The image is polygon ABCD, and A has coordinates (10, -4). Use the grid shown to draw ABCD and find the area of polygon ABCD. 8.3(B), 8.10(D)

y

xO

-2

-4-3

-2-4-3 21 43

1234

AB

CD

15. In the figure below, mACD = mADC = mCDB = 90. What is the value of x in the figure? Explain. 8.3(A)

4 9A

C

D

x

B

35 in.

5:1; a = 1.7 in.; Sample answer: 6.5 _ 1.3 = 5; 8.5 _ 5 = 1.7

(x, y) ( 1 _ 5 x, 1 _ 5 y ) ; F(1, 1)

5.55 gal65 cm 2

6 units; Sample answer:

ACB ADC CDB,so 4 _ x = AC _ CB = x _ 9 x 2 = 36 x = 6

40 sq units

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