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NAME_____________________________________DATE________________PER.________
7.2 – SIMILAR POLYGONS
Use the figures below to answer the questions that follow.
1. __________
∠𝐴 ≅ ?
M
B
2. __________
̅̅̅̅
𝐴𝐵 ∶ ?
3. __________
̅̅̅̅ ∶ ?
𝐶𝐴
4. __________
∠𝑀 ≅ ?
5. __________
∠𝐶 ≅ ?
6. __________
̅̅̅̅̅ ∶ ?
𝑀𝑁
A

C
7. __________
Name the side included between ∠𝐴 and ∠𝐵.
8. __________
̅̅̅̅̅ and 𝐿𝑀
̅̅̅̅ .
Name the angle included between 𝑀𝑁
9. __________
̅̅̅̅ .
Name the angle included between ̅̅̅̅
𝐴𝐶 and 𝐵𝐶
10. __________
Name the side included between ∠𝐿 and ∠𝑁.
If 𝑸𝒖𝒂𝒅 𝑳𝑴𝑵𝑶 is similar to 𝑸𝒖𝒂𝒅 𝑾𝑿𝒀𝒁, name the following.
11. __________
∠𝐿 ≅ ?
12. __________
̅̅̅̅̅ ∶ ?
𝑀𝑁
13. __________
∠𝑁 ≅ ?
14. __________
̅̅̅̅̅ ∶ ?
𝑍𝑊
15. __________
̅̅̅̅̅ and 𝑋𝑌
̅̅̅̅?
What angle is included between 𝑊𝑋
16. __________
What side is included between ∠𝑁 and ∠𝑂?
L
N
17. a) ∠𝐴 ≅__________
𝐴𝐵𝐶𝐷~𝑊𝑋𝑌𝑍 below. Use these figures to answer the questions.
b) ∠𝐵 ≅ _________
A
B
c) ∠𝐶 ≅ __________
W
X
d) ∠𝐷 ≅ _________
e)
𝐴𝐵
=
18. YES
𝑍𝑌
or
=
NO
Z
C
D
𝐵𝐶
Y
Are the two triangles shown below similar?
F
C
Explain:
8 𝑖𝑛
A
12 𝑖𝑛
110° 38°
6 𝑖𝑛
12 𝑖𝑛
18 𝑖𝑛
32°
B
D
110°
E
9 𝑖𝑛
19. __________
What is the scale factor of ∆𝐹𝐷𝐸 to ∆𝐶𝐴𝐵 in problem #2?
20. __________
What is the ratio of the perimeter of ∆𝐹𝐷𝐸 to ∆𝐶𝐴𝐵?
21. __________
How do the scale factor and ratio of the perimeters of ∆𝐹𝐷𝐸 to ∆𝐶𝐴𝐵
compare?
For each of the following, each pair of polygons is similar. Find the values of ‘𝒙’ and ‘𝒚’.
F
22. 𝑥 = _________
𝑦 =__________
A
15
𝑥 + 2
D
B
8
𝑦−3
5
10
C
H
I
H
23. 𝑥 = __________
G
E
M
𝟗𝟖°
𝑦 = __________
G
𝟖𝟕°
N
(𝒚 + 𝟑𝟎)°
J
L
(𝒙 − 𝟒𝟎)°
𝟔𝟎°
O
K
24. 𝑥 = __________
𝟔
𝑦 = __________
𝒚°
R
𝟏𝟐
𝟒
𝒙
𝟑𝟎°
𝟖𝟎°
J
L Q
25. 𝑥 = __________
T
D
𝟏𝟎 𝒄𝒎
𝑦 = __________
G
𝟏𝟐 𝒄𝒎
𝟐𝟎 𝒄𝒎
𝟏𝟐 + 𝒙
E
𝟏𝟐 𝒄𝒎
S
A
𝒚
A
26. 𝑥 = __________
𝑦 = __________
S
T
𝟑 𝒊𝒏
L
𝟏𝟎 𝒊𝒏
𝟔 𝒊𝒏
𝒚
C
𝟔 𝒊𝒏
N
E
𝒙
A
27. 𝑥 = __________
𝑦 = __________
D
𝟗
𝟑
𝟐
M
𝒙+𝟒
C I
𝒚
𝟒
S
Solve each of the following.
28. Measures (6):
The sum of the measures of the interior angles of a hexagon is 720°.
The measures of the angles of a particular hexagon are in the ratio
4: 5: 5: 8: 9: 9. What are the measures of these angles?
29. Measures (2):
The ratio of the measure of two complementary angles is 4: 5. What
are the measures of the angles?
REVIEW PROBLEMS
Solve for ‘𝒙’ in each of the following.
30. 𝑥 = __________
𝑥 + 6 5𝑥
=
3
9
31. 𝑥 = __________
2𝑥 − 7 12 − 7𝑥
=
9
6
Set up a proportion and solve.
32. __________
For field trips, the Brighton School requires that the teacher to student
ratio be at least 2: 15. If there are 45 students on a field trip, what is the
least number of teachers needed to supervise?
33. __________
Recall that the slope of a line is a ratio of the rise to the run. If a line
has a slope of
3
, and you have chosen two points on the line that have
5
a rise of 15, what is the run?
Find the correct answer for each of the following. Clearly circle your answers. Work
must be shown in order to receive credit.
34. Which of the following statements is true?
A. If two figures are similar, then they are congruent.
B. If two figures are congruent, then they are similar.
C. If two figures are similar, then their corresponding sides have the same length.
D. Not Here
35. The angles of a triangle are in the ratio of 3: 4: 5. What is the degree measure of the
smallest angle of the triangle?
36. The copy machine in the math workroom can make a copy of a document every 3
seconds. How many copies can it make in 17 minutes?
A. 1024
B. 340
C. 240
D. 51