Chapter 7 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. If
then 3a = ____.
a. 3b
____
c. 5b
d. 6b
c.
d.
b.
c.
d.
a. 54
b. 81
c. 9
d. 18
a.
b. 5
c. 1
d. 25
a. –3
b.
c.
d. 3
a.
b.
c.
d.
2. If
b. 10b
, which equation must be true?
a.
____
b.
3. If
, then
a.
= ____.
Solve the proportion.
____
____
____
____
____
4.
5.
6.
7.
8. Figure
a.
____
1
25
. Name a pair of corresponding sides?
b.
9. Determine whether the figures are similar.
c.
d.
7.5
1.5
3
3
4.65
4.65
7.5
1.5
Not drawn to scale
a. similar
b. not similar
c. not enough information
Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.
____ 10. In RST, RS = 10, RT = 15, and mR = 32. In UVW, UV = 12, UW = 18, and mU = 32.
a.
c.
;
;
b.
d. The triangles are not similar.
;
____ 11. In QRS, QR = 4, RS = 15, and mR = 36. In UVT, VT = 8, TU = 32, and mT = 36.
a.
c.
;
;
b.
d. The triangles are not similar.
;
____ 12. ABCD ~ WXYZ. AD = 6, DC = 3, and WZ = 59. Find YZ. The figures are not drawn to scale.
X
B
W
A
Y
C
D
Z
a. 118
b. 29.5
c. 21.7
d. 177
The polygons are similar, but not necessarily drawn to scale. Find the values of x and y.
____ 13.
a.
x=
,y=
c.
x = 9, y =
b.
x=
d. x = 9, y = 27
, y = 27
____ 14. Triangles ABC and DEF are similar. Find the lengths of AB and EF.
A
D
5x
5
x F
E
B
4
C
a. AB = 2; EF = 10
b. AB = 10; EF = 2
c. AB = 20; EF = 4
d. AB = 4; EF = 20
____ 15. Write a similarity statement for the triangles.
D
53°
G
60°
67°
60°
C
E
F
H
a.
b.
c.
d.
____ 16. Are the triangles similar? If so, explain why.
30.4°
84.6°
84.6°
a. yes, by SAS
____ 17.
65°
b. yes, by SSS
What is the measure of
c. yes, by AA
d. no
c. 250
d. 35
?
R
)
U
)
47°
))63°
Q
a. 70
))
S
T
V
b. 110
State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you
used.
____ 18. In QRS, QR = 16, RS = 64, and mR = 29. In UVT, VT = 8, TU = 32, and mT = 29.
a.
c.
; ASA
; ASA
b.
d. The triangles are not similar.
; SAS
____ 19.
B
O
5
12
M
5
7.5
8
A
7.5
C
N
a.
b.
; SSS
; SAS
c.
; AA
d. The triangles are not similar.
a.
b.
; SAS
; SAS
c.
; SSS
d. The triangles are not similar.
____ 20.
Explain why the triangles are similar. Then find the value of x.
____ 21.
)
x
7
)
12
8
Not drawn to scale
a.
1
2
b.
1
AA Postulate; 10
2
SSS Postulate; 10
c.
2
3
d.
2
AA Postulate; 4
3
SAS Postulate; 4
____ 22. Use the information in the diagram to determine the height of the tree to the nearest foot.
a. 80 ft
b. 264 ft
c. 60 ft
d. 72 ft
Find the geometric mean of the pair of numbers.
____ 23. 175 and 7
a. 55
b. 45
c. 35
____ 24. 5 and 6
a. 30
b. 6
c.
d. 40
35
d.
30
Solve for a and b.
____ 25.
)
8
10
6
a
)
b
a.
c.
b.
d.
____ 26.
)
21
29
20
a
)
b
____ 27.
a.
c.
b.
d.
Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
7
21
a. 28
b. 7 3
c. 147
____ 28. Use the Side-Splitter Theorem to find x, given that
d. 2 7
.
A
8
P
12
Q
x
18
B
C
a. 12
b. 6
____ 29. Given:
c. 20
. Find the length of
d. 24
. The diagram is not drawn to scale.
A
6
P
Q
12
18
B
C
a. 11
b. 12
____ 30. Given
c. 18
d. 9
, solve for x.The diagram is not drawn to scale.
A
x B
11
E 5 D
a.
7
C
b.
____ 31. Find the value of x, given that
c.
.
d.
O
P
9
N
x
Q
18
20
M
a. x = 10
b. x = 20
c. x = 13
d. x = 25.5
Solve for x.
____ 32.
x– 2
x
x+ 5
>
x+ 1
>
a. 5
b. 2.5
c. 7.5
d. 10
b. 24
c. 2 6
d.
b.
c.
d.
____ 33.
x
3
8
Not drawn to scale
a. 11
33
____ 34.
x
7
13
a.
____ 35.
bisects
, LM = 18, NO = 4, and LN = 10. Find OM.
N
O
L
a. 7.2
M
b. 45
____ 36. Find x to the nearest tenth.
c. 5.43
d. 2.22
8.3
x
6.7
)) )
)
11.6
Not drawn to scale
a. 4.8
b. 14.4
c. 9.4
Short Answer
37.
. Complete the statements.
A
G
E
B
F
H
D
J
C
a.
GH
b.

AB
DJ
Essay
38. Write a proof.
Given:
Prove:
A
D
B
E
C
d. 1.7
Chapter 7 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: C
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 2
2. ANS: B
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 2
3. ANS: C
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 2
4. ANS: C
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 3
5. ANS: D
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 3
6. ANS: A
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 3
7. ANS: D
REF: 7-1 Ratios and Proportions
TOP: 7-1 Example 3
8. ANS: D
REF: 7-2 Similar Polygons
TOP: 7-2 Example 1
9. ANS: B
REF: 7-2 Similar Polygons
TOP: 7-2 Example 2
10. ANS: B
REF: 7-2 Similar Polygons
TOP: 7-2 Example 2
11. ANS: D
REF: 7-2 Similar Polygons
TOP: 7-2 Example 2
12. ANS: B
REF: 7-2 Similar Polygons
TOP: 7-2 Example 3
13. ANS: D
REF: 7-2 Similar Polygons
TOP: 7-2 Example 3
14. ANS: B
REF: 7-2 Similar Polygons
TOP: 7-2 Example 3
15. ANS: C
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 1
16. ANS: C
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 2
17. ANS: A
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 1
18. ANS: B
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 2
19. ANS: A
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 2
20. ANS: A
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 2
21. ANS: D
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 3
22. ANS: A
REF: 7-3 Proving Triangles Similar
TOP: 7-3 Example 4
23. ANS: C
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 1
24. ANS: D
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 1
25. ANS: A
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 2
26. ANS: A
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 2
27. ANS: B
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 2
28. ANS: A
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 1
29. ANS: D
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 1
30. ANS: A
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 1
31. ANS: A
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 1
32. ANS: A
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 1
33. ANS: D
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 2
34. ANS: A
REF: 7-4 Similarity in Right Triangles
TOP: 7-4 Example 2
35. ANS: A
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 3
36. ANS: B
REF: 7-5 Proportions in Triangles
TOP: 7-5 Example 3
SHORT ANSWER
37. ANS:
; DC
REF: 7-2 Similar Polygons
TOP: 7-2 Example 1
ESSAY
38. ANS:
[4] Answers may vary. Sample:
1.
Given
2.
Prop. of Proportions
3.
4.
Vertical
are .
SAS Theorem
REF: 7-3 Proving Triangles Similar