# Dilations and Similarity #3 ```Name _________________________________ Period_________ Date________________
Created by Corbin/Lyons
Dilations and Similarity #3
1. What does similarity mean as it relates to a figures’ sides and angles?
𝑥
2. What is the missing number?
48
= 56
35
3. 𝐴𝐵𝐶𝐷 ∼ 𝐸𝐹𝐺𝐻.
What measurement would need to be in the denominator
to make the equation true?
? =______
̅̅̅̅ 𝑚𝐷𝐶
̅̅̅̅
𝑚𝐶𝐵
=
̅̅̅̅
?
𝑚𝐺𝐹
F
C
B
G
E
H
A
D
3
̅̅̅̅ is 12mm, how long is̅̅̅̅̅
4. If figure 𝐴𝐵𝐶𝐷 (above) is dilated by a scale factor of 4 and 𝑚𝐷𝐶
𝐻𝐺 ?
5. The pair of triangles in the figure are similar. What is the value of x?
25 in.
6 in.
x
y
8 in.
Proportion _______________
Solution____________
Proportion _______________
Solution____________
20 in.
6. Find the value of y in problem #5.
̅̅̅̅ = 42, 𝑚𝐴𝐶
̅̅̅̅ = 30, 𝑎𝑛𝑑 𝑚𝐴𝐷
̅̅̅̅ = 21, then find 𝑚𝐴𝐹
̅̅̅̅ .
7. ∆ 𝐴𝐵𝐶 ~∆ 𝐴𝐷𝐹. If 𝑚𝐴𝐵
A
Proportion _______________
D
B
F
C
Solution____________
8. The hexagons below are similar. Find n.
A
n  ___________
52
B
U
F
V
E
C
12
Z
Y
W
n
X
D
9
9. Triangle ABC is similar to triangle KLM where the ratio of proportionality is
What is KL?
2
, and AB = 12 centimeters.
3
B
L
a. 2 cm
b. 4 cm
c. 8 cm
K
d. 24 cm
A
C
10. The two triangles in the picture (to the right) are similar. What is the value of b?
A. 𝑏 =
3
B. 𝑏 =
𝑎𝑥
𝑎𝑥
3
C.
𝑏=𝑥
11. Triangle 𝐿𝑀𝑁 is similar to Triangle 𝑄𝑃𝑅. If 𝑚∠𝐿 = 25&deg; and 𝑚∠𝑁 = 40&deg;, find 𝑚∠𝑄&deg;.
12. If ∆𝑈𝑉𝑊 ≅ ∆𝑋𝑌𝑍, which of the following is true?
A.
B.
C.
D.
∠𝑉 ≅ ∠𝑍
∠𝑉 ≅ ∠𝑋
∠𝑌 ≅ ∠𝑈
∠𝑊 ≅ ∠𝑍
Draw two triangles on the grid that show this similarity.
M
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