Transcript Chapter 7 Practice Exam
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
7-1 56% 28% 17% A.
B.
C.
0% D.
c. 120 : 7 7-1 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.
B.
6% C.
0% D.
B. 50 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?
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 50 o Correct answer is B.
3.
๐ ๐
=
๐ ๐๐
A. 24
๐
B.
C. 6
๐๐
D.
๐ ๐
89% A.
0% B.
6% 6% C.
D.
7-1
A. 24
3.
๐ ๐
=
๐ ๐๐
๐๐ = ๐๐๐
Cross Product
๐ = ๐๐
Division Property Correct answer is A.
7-1
4. Given the proportion
๐ ๐ = ๐ ๐๐
, what ratio completes the equivalent proportion
๐ ๐ = ๐
A.
๐๐ ๐
B.
๐๐ ๐
C.
๐๐ ๐๐
44% 44%
D.
๐
? 7-1 6% 6% A.
B.
C.
D.
B.
๐ ๐๐
4. Given the proportion
๐ ๐ = ๐ ๐๐
, what ratio completes the equivalent proportion
๐ ๐ =
? 7-1 Exchange the means
๐ = ๐ ๐ ๐๐ ๐ = ๐ ๐ ๐๐
Correct answer is B.
D
8
5. Are the polygons similar? If they are, write a similarity statement and give the scale factor.
A
20.8
20.8
C
8
B N
5.7
M
1.9
1.9
L K
A.
B.
5.7
C.
D.
๐จ๐ฉ๐ช๐ซ ๏พ ๐ต๐ฒ๐ณ๐ด; ๐: ๐. ๐ ๐จ๐ฉ๐ช๐ซ ๏พ ๐ฒ๐ณ๐ด๐ต; ๐๐. ๐: ๐. ๐ ๐จ๐ฉ๐ช๐ซ ๏พ ๐ฒ๐ณ๐ด๐ต; ๐: ๐. ๐
The polygons are not similar.
Not drawn to scale.
7-2 44% 33% 11% 11% A.
B.
C.
D.
D. The polygons are not similar.
7-2 5. Are the polygons similar? If they are, write a similarity statement and give the scale factor.
N A
20.8
B
1.9
K
8 8 5.7
5.7
M D C
20.8
1.9
L
Not drawn to scale.
All of the angles are the same The sides are not in proportion.
8 1.9
โ 20.8
5.7
A
8
6. The polygons are similar, but not necessarily drawn to scale. Find the value of x.
K B
A.
๐๐๐
B.
๐๐. ๐
J L
C.
๐๐๐ 4
C
55
D.
๐๐. ๐
x
7-2
D
89%
M
0% A.
B.
11% C.
0% D.
๐ฉ. ๐๐. ๐
6. The polygons are similar, but not necessarily 7-2 drawn to scale. Find the value of x.
K B A
8
D
4
J C
55
M x L
๐ ๐๐ = ๐ ๐ ๐๐ = ๐๐๐ ๐ = ๐๐. ๐
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 of paper that is 8
๐ ๐
in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
๐ ๐
A.
๐
in. by
๐
in.
๐ ๐ B. ๐ ๐ ๐
in. by
๐ ๐ ๐
in.
C. ๐ ๐ ๐
in. by
๐๐ ๐ ๐
in.
D. ๐ ๐ ๐
in. by
๐๐ ๐ ๐
in 33% 28% 39% 7-2 A.
B.
C.
0% D.
๐. ๐ ๐ ๐
in. by
๐๐ ๐ ๐
in 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 of paper that is 8
๐ ๐
in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
Case 1:
๐
Set
๐๐ = ๐ ๐
Case 2:
๐
Set
๐.๐ = ๐ ๐ ๐๐๐๐๐ ๐ < ๐. ๐ ๐๐๐๐๐ ๐ < ๐๐ ๐๐ = ๐๐ ๐ ๐ = ๐ ๐
NOT POSSIBLE
๐๐ = ๐๐ ๐ = ๐๐. ๐
Correct answer is C.
๐ ๐
in. by
๐๐ ๐
in
๐ ๐
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.
๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ ๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐
7-2 67% 22% A.
B.
6% 6% C.
D.
๐ฉ. ๐๐ ๐๐๐๐๐๐๐๐๐๐๐
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?
๐ ๐๐๐ = ๐ ๐๐๐๐ ๐๐๐๐ = ๐๐๐๐ ๐ = ๐๐
The correct answer is B. 18 millimeters
9. Are the two triangles similar? How do you know?
J H
A. yes, by AA
๏พ 42 ยฐ
M
42 ยบ
B. no C. yes, by SAS
๏พ
D. yes, by SSS
๏พ
K
7-3 50%
G
28% 22% A.
B.
C.
0% D.
A. yes, by AA
๏พ
7-3 9. Are the two triangles similar? How do you know?
J H
42 ยฐ
M
42 ยบ
G
โ ๐ฏ โ โ ๐ฒ
K
โ ๐ฏ๐ด๐ฎ โ โ ๐ฑ๐ด๐ฒ ๐จ๐จ~
O
10. State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used.
33
J
11
M
7-3 44%
21
K
7
N
A.
B.
C.
โ๐ถ๐ด๐ต~โ๐ถ๐ฑ๐ฒ; ๐บ๐จ๐บ~ โ๐ถ๐ด๐ต~โ๐ฑ๐ฒ๐ถ; ๐บ๐จ๐บ~ โ๐ถ๐ด๐ต~โ๐ถ๐ฑ๐ฒ; ๐บ๐บ๐บ~
D. The triangles are not similar.
28% 22% 6% A.
B.
C.
D.
๐จ. โ๐ถ๐ด๐ต~โ๐ถ๐ฑ๐ฒ; ๐บ๐จ๐บ~
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
7
N
โ ๐ถ โ โ ๐ถ ๐๐๐๐๐ ๐๐ ๐๐๐๐๐๐๐๐๐ ๐๐ ๐๐ โ ๐๐ ๐๐ ๐๐๐ =
924 So the triangles are similiar by S
๐๐~ ๐จ. โ๐ถ๐ด๐ต~โ๐ถ๐ฑ๐ฒ; ๐บ๐จ๐บ~
11. Which theorem or postulate proves the two triangles are similar?
A. SSS Theorem
10 5 20 > >
B. SAS Theorem C. AS Postulate D. AA Postulate
44% 7-3 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 >
Therefore, the triangles are similar by AA
~
correct answer is D.
Not drawn to scale.
13. What are the values of a and b?
)
a
) 16 4
A.
B.
C.
D.
๐ = ๐; ๐ = ๐ ๐ ๐ = ๐๐; ๐ = ๐ ๐ ๐ = ๐; ๐ = ๐ ๐ ๐ = ๐๐; ๐ = ๐๐
7-4
b
50% 39% 11% A.
B.
C.
0% D.
๐ช. ๐ = ๐; ๐ = ๐ ๐
13. What are the values of a and b?
) 16
a
)
b
4 ๐๐ = ๐ ๐ ๐ ๐ช๐๐๐๐ ๐๐๐๐ ๐๐๐ ๐ ๐ ๐ = ๐ = ๐๐ ๐ ๐ = ๐ ๐๐ ๐ช๐๐๐๐ ๐๐๐๐ ๐๐๐ ๐ ๐ = ๐๐ ๐ = ๐ ๐
Correct answer is C.
7-4
14. Find the geometric mean of the pair of numbers.
90 and 10 A.
๐๐๐
B.
๐๐
C.
๐๐
D.
๐๐
7-4 61% 22% 11% A.
B.
6% C.
D.
B.
๐๐
14. Find the geometric mean of the pair of numbers.
90 and 10
๐๐ = ๐ ๐ ๐๐
7-4
๐
๐
= ๐๐๐ ๐ = ๐๐
Correct Answer is B.
15. Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale.
A.
๐ ๐
B.
๐๐
C.
๐๐
D.
๐๐
7-4
5 16
44% 17% 22% 17% A.
B.
C.
D.
๐จ. ๐ ๐
15. Find the length of the altitude drawn to the 7-4 hypotenuse. The triangle is not drawn to scale.
๐ ๐ = ๐ ๐๐ ๐
๐
= ๐๐
5 16
๐ = ๐ ๐
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 Kristenโs 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
A.
B.
C.
D.
How far is the library from the park?
How far is the park from the football field?
๐๐
miles;
๐๐
miles
๐
miles;
๐๐. ๐
miles
๐ ๐
miles;
๐ ๐๐
miles
๐ ๐
miles;
๐๐
miles 44%
9 miles 5 miles Library
7-4
Football field
28% 17% 11% A.
B.
C.
D.
C.
๐ ๐
miles;
๐ ๐๐
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 Kristenโs 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?
๐ ๐ = ๐ ๐ ๐ ๐ = ๐ ๐๐
5 miles Library 9 miles
๐
๐
= ๐๐ ๐
๐
= ๐๐๐
Football field
๐ = ๐ ๐ ๐ = ๐ ๐๐
Correct answer is C.
17. What is the value of x, given that
๐ท๐ธ โฅ ๐ฉ๐ช
A
A.
๐
x
7
B.
๐๐
P Q
C.
๐๐
35 40
D. 16
?
7-5
B C
71% A.
18% 12% B.
C.
0% D.
A.
๐
17. What is the value of x, given that
๐ท๐ธ โฅ ๐ฉ๐ช
๐
A
= ๐ ๐๐ ๐๐
x
7
?
P Q
๐๐๐ = ๐๐๐
35 40
7-5
๐ = ๐
B C
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.
๐๐ ๐๐๐๐ ๐ PLOT 1 48 yards PLOT 2 Shelby Road PLOT 3 64 yards PLOT 4
B.
C.
๐๐ ๐ ๐ ๐๐ ๐ ๐
D. 7
๐ ๐ ๐ ๐๐๐๐ ๐ ๐๐๐๐ ๐ ๐๐๐๐ ๐
7-5 0% A.
0% B.
0% C.
0% D.
๐ช. ๐๐ ๐ ๐ ๐๐๐๐ ๐
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?
40 yards Cheshire Road
48 64 = 40 ๐ฅ
PLOT 1 PLOT 2 PLOT 3 PLOT 4
48๐ฅ = 2560
Shelby Road 48 yards 64 yards
53.333333
Correct answer is C.
19. What is the value of x to the nearest tenth?
4.6
x
5.1
A.
B.
C.
๐. ๐ ๐. ๐
)) )) 12.2
Not drawn to scale.
D.
๐๐. ๐ ๐๐
7-5 0% A.
0% B.
0% C.
0% D.
D.
๐๐
19. What is the value of x to the nearest tenth?
7-5
4.6
x
5.1
)) )) 12.2
Not drawn to scale.
๐ ๐. ๐ = ๐๐. ๐ ๐. ๐ ๐. ๐๐ = ๐๐. ๐๐ ๐๐
.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.
๐๐. ๐ ๐๐; ๐. ๐ ๐๐
B.
๐. ๐ ๐๐; ๐. ๐ ๐๐
C.
๐๐ ๐๐; ๐. ๐ ๐๐
D.
๐๐. ๐ ๐๐; ๐. ๐ ๐๐
7-5 0% A.
0% B.
0% C.
0% D.
B.
๐. ๐ ๐๐; ๐. ๐ ๐๐
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 7.9
= 5 ๐ฅ or 5 7.9
= 6 ๐ฆ 6๐ฅ = 39.5
5๐ฆ = 47.4
๐ฅ = 6.58333
๐ฆ = 9.48
Correct answer is B. 6.6 cm shortest and 9.5 cm longest.