Chapter 7 Practice Exam
Questions similar to the Chapter 7 Exam
1. A model is made of a car. The car is 10 feet long and
the model is 7 inches long. What is the ratio of the length
of the car to the length of the model? A. 10 : 7
B. 7 : 120
C. 120 : 7
D. 7 : 10
56%
28%
17%
0%
A.
B.
C.
D.
7-1
7-1
c. 120 : 7
1. A model is made of a car. The car is 10 feet long and
the model is 7 inches long. What is the ratio of the length
of the car to the length of the model?
First in a ratio units must match
Covert 10 feet to 120 inches
Car / Model = 120 / 7
Reduce if possible
Answer is 120:7
Correct answer is C
2. The measures of the angles of a triangle are
in the extended ratio 5 : 6 : 7. What is the
measure of the smallest angle?
A. 60
B. 50
C. 10
D. 70
7-1
83%
11%
A.
6%
B.
C.
0%
D.
7-1
2. The measures of the angles of a triangle are
in the extended ratio 5 : 6 : 7. What is the
measure of the smallest angle?
B. 50
Since it is angles they add up to 180 degrees.
Think of the ratio as 5x : 6x : 7x
So 5x + 6x + 7x = 180
18x = 180
x =10
Angles are 50, 60, and 70
Smallest angle is 50o
Correct answer is B.
3.
𝟒
𝟗
=
𝒎
𝟓𝟒
A. 24
B.
𝟏
𝟐𝟒
C. 6
D.
𝟐
𝟑
7-1
89%
0%
A.
B.
6%
C.
6%
D.
A. 24
3.
𝟒
𝟗
=
7-1
𝒎
𝟓𝟒
𝟗𝒎 = 𝟐𝟏𝟔 Cross Product
𝒎 = 𝟐𝟒
Division Property
Correct answer is A.
𝒂
𝒃
4. Given the proportion =
completes the equivalent
A.
B.
C.
D.
𝒂
𝟏𝟗
𝒃
𝟏𝟗
𝟓
𝟏𝟗
𝟏𝟗
𝒃
𝟓
𝟏𝟗
, what ratio
𝒂
proportion
𝟓
=
?
7-1
44%
6%
A.
44%
6%
B.
C.
D.
B.
𝒃
𝟏𝟗
𝒂
𝒃
4. Given the proportion =
completes the equivalent
𝟓
𝟏𝟗
, what ratio
𝒂
proportion
𝟓
Exchange the means
𝒂
𝟓
=
𝒃 𝟏𝟗
𝒂
𝒃
=
𝟓 𝟏𝟗
Correct answer is B.
7-1
=
?
5. Are the polygons similar? If they are, write a
similarity statement and give the scale factor.
A
20.8
B
N
1.9
A.
B.
5.7 C.
D.
K
8
D
8
20.8
C
5.7
M
1.9
L
𝑨𝑩𝑪𝑫𝑵𝑲𝑳𝑴; 𝟖: 𝟓. 𝟕
𝑨𝑩𝑪𝑫𝑲𝑳𝑴𝑵; 𝟐𝟎. 𝟖: 𝟏. 𝟗
𝑨𝑩𝑪𝑫𝑲𝑳𝑴𝑵; 𝟖: 𝟏. 𝟗
The polygons are not
similar.
Not drawn to scale.
7-2
44%
33%
11%
A.
11%
B.
C.
D.
7-2
5. Are the polygons similar? If they are, write a
similarity statement and give the scale factor.
D. The polygons are not similar.
A
20.8
N
B
1.9
K
8
8
5.7
5.7
D
20.8
C
M
1.9
L
Not drawn to scale.
All of the angles are the same
The sides are not in proportion.
8
20.8
≠
1.9
5.7
6. The polygons are similar, but not necessarily
drawn to scale. Find the value of x.
K
B
J
A
L
C
8
4
55
A.
B.
C.
D.
𝟐𝟐𝟎
𝟐𝟕. 𝟓
𝟏𝟏𝟎
𝟏𝟓. 𝟖
7-2
x
D
89%
M
11%
0%
A.
0%
B.
C.
D.
𝑩. 𝟐𝟕. 𝟓
6. The polygons are similar, but not necessarily 7-2
drawn to scale. Find the value of x.
K
B
J
A
L
C
8
4
55
x
D
𝟖
𝟒
=
𝟓𝟓 𝒙
M
𝟖𝒙 = 𝟐𝟐𝟎
𝒙 = 𝟐𝟕. 𝟓
Correct answer is B.
7. You want to draw an enlargement of a design that is printed on a
card that is 5 in. by 6 in. You will be drawing this design on an piece
𝟏
of paper that is 8 in. by 11 in. What are the dimensions of the
𝟐
largest complete enlargement you can make?
A.
B.
C.
D.
𝟐
𝟏
𝟏 in. by 𝟒 in.
𝟑
𝟓
𝟏
𝟏
𝟖 in. by 𝟒 in.
𝟐
𝟓
𝟏
𝟏
𝟖 in. by 𝟏𝟎 in.
𝟐
𝟓
𝟐
𝟏
𝟏 in. by 𝟏𝟎 in
𝟑
𝟓
7-2
39%
33%
28%
0%
A.
B.
C.
D.
𝟏
𝟏
𝐂. 𝟖 in. by 𝟏𝟎 in
𝟐
𝟓
7-2
7. You want to draw an enlargement of a design that is printed on a
card that is 5 in. by 6 in. You will be drawing this design on an piece
𝟏
of paper that is 8 in. by 11 in. What are the dimensions of the
𝟐
largest complete enlargement you can make?
Case 2:
Case 1:
𝟓
𝟔
𝟔
𝟓
Set
=
Set
=
𝟏𝟏
𝟖.𝟓
𝒚
𝒙
𝒘𝒉𝒆𝒓𝒆 𝒚 < 𝟖. 𝟓
𝒘𝒉𝒆𝒓𝒆 𝒙 < 𝟏𝟏
𝟔𝒚 = 𝟓𝟓
𝟏
𝒙=𝟗
𝟔
𝟓𝒙 = 𝟓𝟏
𝒙 = 𝟏𝟎. 𝟐
NOT POSSIBLE
Correct answer is C.
𝟏
𝟏
𝟖 in. by 𝟏𝟎 in
𝟐
𝟓
8. In a scale drawing of the solar system, the scale is 1 mm = 500
km. For a planet with a diameter of 9000 kilometers, what should be
the diameter of the drawing of the planet?
A.
B.
C.
D.
𝟏𝟖𝟎 𝒎𝒊𝒍𝒍𝒊𝒎𝒆𝒕𝒆𝒓𝒔
𝟏𝟖 𝒎𝒊𝒍𝒍𝒊𝒎𝒆𝒕𝒆𝒓𝒔
𝟒𝟓𝟎𝟎𝟎𝟎𝟎 𝒎𝒊𝒍𝒍𝒊𝒎𝒆𝒕𝒆𝒓𝒔
𝟗𝟎𝟎𝟎 𝒎𝒊𝒍𝒍𝒊𝒎𝒆𝒕𝒆𝒓𝒔
7-2
67%
22%
6%
A.
B.
C.
6%
D.
𝑩. 𝟏𝟖 𝒎𝒊𝒍𝒍𝒊𝒎𝒆𝒕𝒆𝒓𝒔
7-2
8. In a scale drawing of the solar system, the scale is 1 mm = 500
km. For a planet with a diameter of 9000 kilometers, what should be
the diameter of the drawing of the planet?
𝟏
𝒙
=
𝟓𝟎𝟎 𝟗𝟎𝟎𝟎
𝟓𝟎𝟎𝒙 = 𝟗𝟎𝟎𝟎
𝒙 = 𝟏𝟖
The correct answer is B. 18
millimeters
9. Are the two triangles similar? How do you know?
J
A.
B.
C.
D.
H
42 °
M
42 º
K
yes, by AA
no
yes, by SAS
yes, by SSS
7-3
50%
G
28%
22%
0%
A.
B.
C.
D.
A. yes, by AA
7-3
9. Are the two triangles similar? How do you know?
J
H
42 °
M
42 º
G
∠𝑯 ≅ ∠𝑲
∠𝑯𝑴𝑮 ≅ ∠𝑱𝑴𝑲
𝑨𝑨~
K
10. State whether the triangles are similar. If so, write a similarity
statement and the postulate or theorem you used.
O
33
J
21
K
7
N
44%
28%
22%
6%
A.
B.
C.
D.
M
11
A.
B.
C.
D.
7-3
∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑨𝑺~
∆𝑶𝑴𝑵~∆𝑱𝑲𝑶; 𝑺𝑨𝑺~
∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑺𝑺~
The triangles are not
similar.
𝑨. ∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑨𝑺~
7-3
10. State whether the triangles are similar. If so, write a similarity
statement and the postulate or theorem you used.
O
33
J
11
M
21
K
∠𝑶 ≅ ∠𝑶 𝒂𝒏𝒈𝒍𝒆 𝒊𝒔 𝒄𝒐𝒏𝒈𝒓𝒖𝒆𝒏𝒕
7
N
𝟐𝟏 𝟑𝟑
≅
𝟐𝟖 𝟒𝟒
𝟗𝟐𝟒 = 924
So the triangles are similiar by S𝐀𝐒~
𝑨. ∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑨𝑺~
11. Which theorem or postulate proves the two
triangles are similar?
A. SSS Theorem
10
B. SAS Theorem
20
C. AS Postulate
>
D. AA Postulate
5
7-3
>
44%
28%
Not drawn to scale.
22%
6%
A.
B.
C.
D.
D. AA Postulate
7-3
11. Which theorem or postulate proves the two
triangles are similar?
10
20
>
Since the lines are parallel;
the corresponding angles
are congruent.
5
>
Not drawn to scale.
Therefore, the triangles are
similar by AA ~ correct
answer is D.
13. What are the values of a and b?
A. 𝒂 = 𝟖; 𝒃 = 𝟖 𝟓
)
16
B. 𝒂 = 𝟏𝟖; 𝒃 = 𝟒 𝟓
a
4
)
C. 𝒂 = 𝟖; 𝒃 = 𝟒 𝟓
D. 𝒂 = 𝟔𝟒; 𝒃 = 𝟖𝟎
b
50%
39%
11%
0%
A.
B.
C.
D.
7-4
7-4
𝑪. 𝒂 = 𝟖; 𝒃 = 𝟒 𝟓
13. What are the values of a and b?
)
16
𝟏𝟔
𝒂
=
𝒂
𝟒
𝑪𝒓𝒐𝒔𝒔 𝒑𝒓𝒐𝒅𝒖𝒄𝒕 𝒂𝟐 = 𝟔𝟒
𝒂=𝟖
a
4
)
b
𝟒
𝒃
=
𝒃 𝟐𝟎
𝑪𝒓𝒐𝒔𝒔 𝒑𝒓𝒐𝒅𝒖𝒄𝒕 𝒃𝟐 = 𝟖𝟎
𝒃=𝟒 𝟓
Correct answer is C.
14. Find the geometric mean of the pair of numbers.
90 and 10
A.
B.
C.
D.
𝟖𝟎𝟎
𝟑𝟎
𝟒𝟎
𝟑𝟓
7-4
61%
22%
11%
6%
A.
B.
C.
D.
B. 𝟑𝟎
14. Find the geometric mean of the pair of numbers.
90 and 10
𝟗𝟎
𝒙
=
𝒙
𝟏𝟎
𝟐
𝒙
= 𝟗𝟎𝟎
𝒙 = 𝟑𝟎
Correct Answer is B.
7-4
15. Find the length of the altitude drawn to the
hypotenuse. The triangle is not drawn to scale.
A. 𝟒 𝟓
B. 𝟐𝟏
C. 𝟖𝟎
𝟐𝟏
D.
5
7-4
16
44%
22%
17%
A.
B.
17%
C.
D.
7-4
15. Find the length of the altitude drawn to the
hypotenuse. The triangle is not drawn to scale.
𝑨. 𝟒 𝟓
𝟓
𝒙
=
𝒙 𝟏𝟔
5
16
𝒙𝟐 = 𝟖𝟎
𝒙=𝟒 𝟓
Correct answer is A.
16. Kristen lives directly east of the park. The football field is directly south of the park. The
library sits on the line formed between Kristen’s home and the football field at the exact
point where an altitude to the right triangle formed by her home, the park, and the
football field could be drawn. The library is 5 miles from her home. The football field is 9
Park
Home
miles from the library.
How far is the library from the park?
How far is the park from the football field?
5 miles
Library
A.
B.
𝟏𝟒 miles; 𝟐𝟑 miles
𝟕 miles; 𝟏𝟏. 𝟓miles
C.
𝟑 𝟓 miles; 𝟑 𝟏𝟒 miles
D.
𝟑 𝟓 miles; 𝟐𝟑 miles
9 miles
44%
Football field
28%
17%
11%
A.
B.
C.
D.
7-4
C. 𝟑 𝟓 miles; 𝟑 𝟏𝟒 miles
7-4
16. Kristen lives directly east of the park. The football field is directly south of the park.
The library sits on the line formed between Kristen’s home and the football field at the
exact point where an altitude to the right triangle formed by her home, the park, and the
football field could be drawn. The library is 5 miles from her home. The football field is 9
miles from the library.
Park
Home
How far is the library from the park?
How far is the park from the football field?
𝟗 𝒙
=
𝒙 𝟓
𝟐
𝒙 = 𝟒𝟓
5 miles
𝟗
𝒚
=
𝒚 𝟏𝟒
Library
9 miles
𝒙𝟐 = 𝟏𝟐𝟔
Football field
𝒙=𝟑 𝟓
𝒙 = 𝟑 𝟏𝟒
Correct answer is C.
17. What is the value of x, given that 𝑷𝑸 ∥ 𝑩𝑪 ?
A
7
P
35
B
A.
B.
C.
D.
x
Q
40
C
𝟖
𝟏𝟏
𝟏𝟎
16
71%
18%
12%
0%
A.
B.
C.
D.
7-5
7-5
A. 𝟖
17. What is the value of x, given that 𝑷𝑸 ∥ 𝑩𝑪 ?
𝟕
𝒙
=
𝟑𝟓 𝟒𝟎
A
7
P
35
B
x
Q
𝟑𝟓𝒙 = 𝟐𝟖𝟎
40
C
𝒙=𝟖
Correct Answer is A.
18. Plots of land between two roads are laid out according to the
boundaries shown. The boundaries between the two roads are
parallel. What is the length of Plot 3 along Cheshire Road?
40
yards
Cheshire Road
A.
PLOT 4
>
PLOT 3
>
PLOT 2
>
PLOT 1
>
>
B.
C.
48
yards
Sh elb y
R
D.
o ad
𝟕𝟒 𝒚𝒂𝒓𝒅𝒔
𝟐
𝟑
𝟏
𝟓𝟑 𝒚𝒂𝒓𝒅𝒔
𝟑
𝟒
7𝟔 𝒚𝒂𝒓𝒅𝒔
𝟓
𝟒𝟐 𝒚𝒂𝒓𝒅𝒔
64
yards
0%
A.
0%
B.
0%
C.
0%
D.
7-5
𝑪. 𝟓𝟑
𝟏
𝒚𝒂𝒓𝒅𝒔
𝟑
7-5
18. Plots of land between two roads are laid out according to the
boundaries shown. The boundaries between the two roads are
parallel. What is the length of Plot 3 along Cheshire Road?
PLOT 4
>
PLOT 3
48 40
=
64
𝑥
>
PLOT 2
>
PLOT 1
Cheshire Road
>
>
40
yards
48𝑥 = 2560
48
yards
Sh elb y
R
o ad
64
yards
53.333333
Correct answer is C.
19. What is the value of x to the nearest tenth?
4.6
x
))
))
5.1
12.2
Not drawn to scale.
A. 𝟏. 𝟗
B. 𝟐. 𝟒
C.
𝟏𝟑. 𝟓
D. 𝟏𝟏
0%
A.
0%
B.
0%
C.
0%
D.
7-5
D. 𝟏𝟏
7-5
19. What is the value of x to the nearest tenth?
4.6
x
))
))
5.1
𝒙
𝟏𝟐. 𝟐
=
𝟒. 𝟔
𝟓. 𝟏
12.2
Not drawn to scale.
𝟓. 𝟏𝒙 = 𝟓𝟔. 𝟏𝟐
𝟏𝟏.00392157
The correct answer is D. 11
20. An angle bisector of a triangle divides the opposite side of the
triangle into segments 6 cm and 5 cm long. A second side of the
triangle is 7.9 cm long. Find the longest and shortest possible
lengths of the third side of the triangle. Round answers to the
nearest tenth of a centimeter.
A.
B.
C.
D.
𝟒𝟕. 𝟒 𝒄𝒎; 𝟗. 𝟓 𝒄𝒎
𝟗. 𝟓 𝒄𝒎; 𝟔. 𝟔 𝒄𝒎
𝟑𝟎 𝒄𝒎; 𝟔. 𝟔 𝒄𝒎
𝟒𝟕. 𝟒 𝒄𝒎; 𝟑. 𝟖 𝒄𝒎 7-5
0%
A.
0%
B.
0%
C.
0%
D.
B. 𝟗. 𝟓 𝒄𝒎; 𝟔. 𝟔 𝒄𝒎
7-5
20. An angle bisector of a triangle divides the opposite side of the
triangle into segments 6 cm and 5 cm long. A second side of the
triangle is 7.9 cm long. Find the longest and shortest possible
lengths of the third side of the triangle. Round answers to the
nearest tenth of a centimeter.
6
5
5
6
=
or
=
7.9
𝑥
7.9
𝑦
6𝑥 = 39.5
5𝑦 = 47.4
𝑥 = 6.58333
𝑦 = 9.48
Correct answer is B. 6.6 cm shortest and
9.5 cm longest.