NAME ___________________________________________________ DATE ______________________ PERIOD ____________
Chapter 2 Test, Form 3A
SCORE _____________
Each pair of polygons is similar. Determine the missing side measures.
1. ABC ˜ XYZ
C
2 mm
10 mm
? mm
Z
4 in.
A
5 mm
6 mm
5.25 in.
3 in.
6 in.
15 mm
2.
Y
B
8.3(A)
7 in.
X
4 mm
10.5 in.
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)
10 ft
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?
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
8.3(A)
78 cm
Q
L
5. Determine whether the triangles are similar
by angle-angle similarity. If so, write a similarity
8.8(D)
statement.
75°
yes; ∠L ∠R and ∠M ∠P, so LMN ˜ RPQ
N
50°
R
M
E
6. In the figure, triangle ABC is similar to triangle DEC.
Determine the distance from point D to point E.
8.3(A)
55°
d yd
D
P
90 yd
60 yd
90 yd
75°
B
A
180 yd
C
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
8.3(A)
that is 15 feet long. How tall is the telephone pole?
_
8 2 ft
3
8. 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?
8.3(A)
1,200 m 2
Course 3 • Chapter 2 Similarity and Dilations
19
NAME ___________________________________________________ DATE ______________________ PERIOD ____________
Chapter 2 Test, Form 3A
SCORE _____________
(continued)
9. A projector transforms the image on a computer screen so that it is dilated by a scale
factor of 7 . The original image on the screen is 10 inches wide. Find the new width
_
2
after it is projected on the wall.
8.3(A)
35 in.
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.
8.3(A)
Find the scale factor the designer used and the value of a. Explain.
5:1; a = 1.7 in.; Sample answer:
6.5
8.5
_
= 5; _ = 1.7
1.3
5
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 , and the dilation will be centered at the origin. Write an algebraic
5
representation for the dilation. Determine the coordinates of the image of point F after
8.3(B), 8.3(C)
the dilation.
_
( _5 _5 )
(x, y) → 1 x, 1 y ; F’(1, 1)
Use a problem-solving model to solve each problem.
12. An E-shaped figure is formed by four
rectangles having areas of 440 square
centimeters, 240 square centimeters,
240 square centimeters, and 120 square
centimeters. Jason dilates the figure by a scale
factor of 1 . What is the total area of the new
4
8.10(D)
E-shaped figure?
_
13. Mark is painting two rectangular doors.
The first door has an area of 150 square feet.
The second door is a dilation of first door
with a scale factor of 1.4. One gallon of paint
will cover 80 square feet. How many gallons
of paint 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 AʹBʹCʹDʹ, and Aʹ has
coordinates (10, -4). Use the grid shown to
draw ABCD and find the area of polygon
8.3(B), 8.10(D)
AʹBʹCʹDʹ.
4
3
2
1
-4-3-2 O
-2
-3
-4
15. In the figure below, m∠ACD = m∠ADC =
m∠CDB = 90˚. What is the value of x in the
8.3(A)
figure? Explain.
C
x
y
D
C
A
1 2 3 4x
B
4
D
9
B
6 units; Sample answer:
A
ACB ˜ ADC ˜ CDB,
x
AC
so 4x =
= ⇒ x 2 = 36 ⇒ x = 6
_ _ _
CB
9
40 sq units
20
Course 3 • Chapter 2 Similarity and Dilations
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
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