Similarity Quiz Review
Name: _________________________________ A#____
TOOLKIT REVIEW:
Describe each triangle similarity theorem; give an example of a pair of triangles labeled with information necessary to
use the theorem, and write a similarity statement to go with your example.
1. Angle-Angle Similarity Theorem:
2. Side-Angle-Side Similarity Theorem:
3. Side-Side-Side:
ARE THEY SIMILAR?
4. Is ΔBAK ~ ΔJOL? Explain why or
why not.
K
36
B
5. Is ΔACE ~ ΔSPY? Explain why or why not.
E
38
Y
A
60
28°
L
28
26
J
50
O
6.
8
3
2
S
12
a) Is ∆𝑁𝑂𝑃~∆𝑀𝑂𝑄? How do you know?
A
78°
64°
64°
P
C
b) Prove that ∆𝑁𝑀𝑂~∆𝑄𝑃𝑂. You may use a two-column proof, a flowchart proof, or a paragraph proof.
7. Find the value of x. Show your work!
x+5
7
x
36 cm
8. Find the value of x. Show your work!
27 cm
2
x
10
9. If a 36 foot tree casts a 28 foot shadow at the same time a nearby building casts a 70 foot shadow, how tall is the
building? Draw a picture and show your work.
10. (HONORS ONLY) Kendra can see the top of her apartment building reflected in a small fish pond in a park across the
street. She is standing 2 m from the pond, and the distance from the pond to the apartment building is 40 m. If
Kendra’s eyes are 150 cm above the ground, how tall is the apartment building? Draw a picture and show your work!
State if the triangles in each pair are similar. If so, state how you know and complete the similarity statement.
11.
12.
13. ∆𝐷𝐸𝐹~∆𝐶𝐵𝐴 and DE=30cm, EF=21cm, AC=220cm, and AB=77cm. Find the length of BC. Draw a diagram and show
your work.
14. Write the Triangle Proportionality Theorem below then use the Theorem to answer the following questions.
Theorem:
a) Use ̅̅̅̅
𝐷𝐸 ∥ ̅̅̅̅
𝐵𝐶 to find the missing value.
b) Use ̅̅̅̅
𝐷𝐸 ∥ ̅̅̅̅
𝐵𝐶 to find the missing value.
c) Determine whether the given information implies ̅̅̅̅
𝐷𝐸 ∥
̅̅̅̅
𝐵𝐶
d) Determine whether the given information implies ̅̅̅̅
𝐷𝐸 ∥
̅̅̅̅
𝐵𝐶
15.
16.
17.
18.
19. State the Midpoint Connector Theorem for Triangles below. Then use the theorem to answer the questions that
follow.
Theorem:
a)
b)
c)
d)