UNIT 3 REVIEW
Name_________________________________ Per __________
2. In ∆𝐴𝐵𝐶, ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐵𝐶 and 𝑚∠𝐶 = 62°. Find 𝑚∠𝐴.
1. Solve for 𝑥.
3. Solve for 𝑥.
𝑥°
4. Which is a possible length for the third side of a triangle
with side lengths 9 and 16?
A. 6
B. 7
C. 18
D. 25
5. Find 𝑚∠𝐷𝐶𝑍.
6. If the point (−9, 8) translates to (4, −3), then
(6, 1) translates to :
7. What is the ratio of similarity of ∆𝑇𝑆𝑅 to ∆𝐹𝐺𝐻?
8. Which triangle similarity postulate or theorem could be
used to prove that the following triangles are similar?
A. AA
B. SSS
C. SAS
D. SSA
̅̅̅̅ ∥ 𝑊𝑉
̅̅̅̅̅, find the value of 𝑥.
9. If 𝐵𝐶
10. Solve for 𝑥. Explain.
𝑥
9
11. Find the perimeter of the figure below if all
angles meet at right angles.
12. Find the measure of the largest angle.
3𝑥 + 7
13. A triangle has been cut out from a circle. Find the
remaining area.
14. Which triangle similarity postulate or theorem could be
used to prve that the following triangles are similar?
A. AA
B. SSS
10
38°
8
C. SAS
15
D. SSA
15. The length of the hypotenuse of a right triangle is 9 and
the length of one leg is 8. What is the length of the other
leg?
16.
a) What is the smallest side?
b) Classify the ∆ by its angles
and sides.
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅ and 𝑚∠𝐶𝐺𝐹 = 132°.
18. In the figure below, 𝐴𝐵
Which of the following statements is false?
17. A survey indicated that 4 out of 5 people like pizza. If
360 people were surveyed, how many like pizza?
A. 𝑚∠𝐵𝐻𝐸 = 132°
B. 𝑚∠𝐵𝐻𝐹 = 48°
C. ∠𝐴𝐻𝐺 and ∠𝐶𝐺𝐹 are
corr. ∠s
D. ∠𝐵𝐻𝐸 and ∠𝐷𝐺𝐹 are
alt. ext. ∠s
19. Which of the following lengths cannot form a triangle?
B
E
H
D
G
F
A
C
20. A circle has been cut from a rectangle. Find the
remaining area.
A. 13, 14, 18
24 m
B. 3, 21, 17
8m
C. 16, 10, 8
D. 4, 7, 9
45°
21. If ∆𝐴𝐵𝐶~∆𝑋𝑌𝑍,
then
𝐴𝐵
𝑋𝑌
=45°
22. Which of the following best provides a counterexample to the assertion below?
All right triangles are isosceles.
50°
45°
45° 45°
43°
A.
B.
C.
D.
?
𝑋𝑍
43°
43°
23. Given M  O , find the perimeter of the triangle.
50°
50°
4x – 9
M
R
38
2x + 11
50°
43°
43°
43°
43°
43°
24. In the right triangle below, 𝐷𝐸 = 5 and
𝐸𝐹 = 13. Find 𝐷𝐹.
50°
B
D
O
E
F
For #25-30, Determine if the pairs of ∆s are similar. If they are ∼, write a similarity statement. List all your reasons.
25.
26.
27.
28.
29.
30.
̅̅̅̅ ∥ 𝐶𝐷
̅̅̅̅
31. Given: 𝐴𝐵
Prove: ∆𝐴𝐵𝐸 ∼ ∆𝐷𝐶𝐸
̅̅̅̅ ;
̅ ∥ 𝐻𝐺
32. Given: 𝐽𝐼
∠F and ∠HIG are right angles
Prove: ∆𝐽𝐹𝐼 ∼ ∆𝐻𝐼𝐺
33. How much shorter is it to get from school to your house
if you don’t stop at In-n-Out first?
34. Solve for x.
x
35. Find the perimeter of the figure below if all angles meet
at right angles.
36. ∆𝑆𝑅𝑇 ∼ ∆𝐹𝐺𝐸. What is the ratio of similarity of ∆𝐹𝐸𝐺
to ∆𝑆𝑇𝑅?
37. Solve for 𝑥 and 𝑦.
38. Find the measure of the smallest angle.
5𝑥 + 4
39. Which of the following side lengths could form a
triangle?
A. 4, 10, 8
40. The length of the hypotenuse of a right triangle is 14 and
the length of one leg is 6. What is the length of the other
leg?
B. 29, 16, 5
C. 33, 11, 55
D. 13, 7, 26
41. What are the possible side lengths for the third side of a
triangle with side lengths12 and 20?
42. If the point (−3, −2) translates to (−6, 1), then
(7, −4) translates to :
43. A Street, B Street, and C Street are parallel streets that
intersect Main Street and City Drive. How long (to the
A isIMain St. between A street and B street?
nearest yard)
44. Which of the following best provides a counterexample
to the assertion below? (figures not drawn to scale!)
All scalene triangles are obtuse.
A.
133°
D
A Street
46°
B.
88°
80 yds
B Street
200 yds
F
C.
160 yds
45°
D.
41°
C Street
H
B
J
72°
45°