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.

𝟒 𝟗

=

𝒎 𝟓𝟒

A. 24

𝟏

B.

C. 6

𝟐𝟒

D.

𝟐 𝟑

89% A.

0% B.

6% 6% C.

D.

7-1

A. 24

3.

𝟒 𝟗

=

𝒎 𝟓𝟒

𝟗𝒎 = 𝟐𝟏𝟔

Cross Product

𝒎 = 𝟐𝟒

Division Property Correct answer is A.

7-1

4. Given the proportion

𝒂 𝒃 = 𝟓 𝟏𝟗

, what ratio completes the equivalent proportion

𝒂 𝟓 = 𝒂

A.

𝟏𝟗 𝒃

B.

𝟏𝟗 𝟓

C.

𝟏𝟗 𝟏𝟗

44% 44%

D.

𝒃

? 7-1 6% 6% A.

B.

C.

D.

B.

𝒃 𝟏𝟗

4. Given the proportion

𝒂 𝒃 = 𝟓 𝟏𝟗

, what ratio completes the equivalent proportion

𝒂 𝟓 =

? 7-1 Exchange the means

𝒂 = 𝒃 𝟓 𝟏𝟗 𝒂 = 𝟓 𝒃 𝟏𝟗

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.

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% 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

≠ 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.

𝟐𝟐𝟎

B.

𝟐𝟕. 𝟓

J L

C.

𝟏𝟏𝟎 4

C

55

D.

𝟏𝟓. 𝟖

x

7-2

D

89%

M

0% A.

B.

11% C.

0% D.

𝑩. 𝟐𝟕. 𝟓

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

𝟖 𝟓𝟓 = 𝟒 𝒙 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 of paper that is 8

𝟏 𝟐

in. by 11 in. What are the dimensions of the largest complete enlargement you can make?

𝟐 𝟏

A.

𝟏

in. by

𝟒

in.

𝟑 𝟓 B. 𝟖 𝟏 𝟐

in. by

𝟒 𝟏 𝟓

in.

C. 𝟖 𝟏 𝟐

in. by

𝟏𝟎 𝟏 𝟓

in.

D. 𝟏 𝟐 𝟑

in. by

𝟏𝟎 𝟏 𝟓

in 33% 28% 39% 7-2 A.

B.

C.

0% D.

𝐂. 𝟖 𝟏 𝟐

in. by

𝟏𝟎 𝟏 𝟓

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

𝟏 𝟐

in. by 11 in. What are the dimensions of the largest complete enlargement you can make?

Case 1:

𝟔

Set

𝟏𝟏 = 𝟓 𝒚

Case 2:

𝟓

Set

𝟖.𝟓 = 𝟔 𝒙 𝒘𝒉𝒆𝒓𝒆 𝒚 < 𝟖. 𝟓 𝒘𝒉𝒆𝒓𝒆 𝒙 < 𝟏𝟏 𝟔𝒚 = 𝟓𝟓 𝟏 𝒙 = 𝟗 𝟔

NOT POSSIBLE

𝟓𝒙 = 𝟓𝟏 𝒙 = 𝟏𝟎. 𝟐

Correct answer is C.

𝟏 𝟖

in. by

𝟏𝟎 𝟏

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% A.

B.

6% 6% C.

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?

𝟏 𝟓𝟎𝟎 = 𝒙 𝟗𝟎𝟎𝟎 𝟓𝟎𝟎𝒙 = 𝟗𝟎𝟎𝟎 𝒙 = 𝟏𝟖

The correct answer is B. 18 millimeters

9. Are the two triangles similar? How do you know?

J H

A. yes, by AA

 42 °

M

42 º

B. no C. yes, by SAS



D. yes, by SSS



K

7-3 50%

G

28% 22% A.

B.

C.

0% 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

K

∠𝑯𝑴𝑮 ≅ ∠𝑱𝑴𝑲 𝑨𝑨~

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.

∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑨𝑺~ ∆𝑶𝑴𝑵~∆𝑱𝑲𝑶; 𝑺𝑨𝑺~ ∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑺𝑺~

D. The triangles are not similar.

28% 22% 6% A.

B.

C.

D.

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

7

N

∠𝑶 ≅ ∠𝑶 𝒂𝒏𝒈𝒍𝒆 𝒊𝒔 𝒄𝒐𝒏𝒈𝒓𝒖𝒆𝒏𝒕 𝟐𝟏 𝟐𝟖 ≅ 𝟑𝟑 𝟒𝟒 𝟗𝟐𝟒 =

924 So the triangles are similiar by S

𝐀𝐒~ 𝑨. ∆𝑶𝑴𝑵~∆𝑶𝑱𝑲; 𝑺𝑨𝑺~

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.

𝒂 = 𝟖; 𝒃 = 𝟖 𝟓 𝒂 = 𝟏𝟖; 𝒃 = 𝟒 𝟓 𝒂 = 𝟖; 𝒃 = 𝟒 𝟓 𝒂 = 𝟔𝟒; 𝒃 = 𝟖𝟎

7-4

b

50% 39% 11% A.

B.

C.

0% D.

𝑪. 𝒂 = 𝟖; 𝒃 = 𝟒 𝟓

13. What are the values of a and b?

) 16

a

)

b

4 𝟏𝟔 = 𝒂 𝒂 𝟒 𝑪𝒓𝒐𝒔𝒔 𝒑𝒓𝒐𝒅𝒖𝒄𝒕 𝒂 𝟐 𝒂 = 𝟖 = 𝟔𝟒 𝟒 𝒃 = 𝒃 𝟐𝟎 𝑪𝒓𝒐𝒔𝒔 𝒑𝒓𝒐𝒅𝒖𝒄𝒕 𝒃 𝟐 = 𝟖𝟎 𝒃 = 𝟒 𝟓

Correct answer is C.

7-4

14. Find the geometric mean of the pair of numbers.

90 and 10 A.

𝟖𝟎𝟎

B.

𝟑𝟎

C.

𝟒𝟎

D.

𝟑𝟓

7-4 61% 22% 11% A.

B.

6% C.

D.

B.

𝟑𝟎

14. Find the geometric mean of the pair of numbers.

90 and 10

𝟗𝟎 = 𝒙 𝒙 𝟏𝟎

7-4

𝒙

𝟐

= 𝟗𝟎𝟎 𝒙 = 𝟑𝟎

Correct Answer is B.

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

D.

𝟐𝟏

7-4

5 16

44% 17% 22% 17% A.

B.

C.

D.

𝑨. 𝟒 𝟓

15. Find the length of the altitude drawn to the 7-4 hypotenuse. The triangle is not drawn to scale.

𝟓 𝒙 = 𝒙 𝟏𝟔 𝒙

𝟐

= 𝟖𝟎

5 16

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 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?

𝟏𝟒

miles;

𝟐𝟑

miles

𝟕

miles;

𝟏𝟏. 𝟓

miles

𝟑 𝟓

miles;

𝟑 𝟏𝟒

miles

𝟑 𝟓

miles;

𝟐𝟑

miles 44%

9 miles 5 miles Library

7-4

Football field

28% 17% 11% A.

B.

C.

D.

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 𝟗 𝒚 = 𝒚 𝟏𝟒

5 miles Library 9 miles

𝒙

𝟐

= 𝟒𝟓 𝒙

𝟐

= 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

A.

𝟖

x

7

B.

𝟏𝟏

P Q

C.

𝟏𝟎

35 40

D. 16

?

7-5

B C

71% A.

18% 12% B.

C.

0% D.

A.

𝟖

17. What is the value of x, given that

𝑷𝑸 ∥ 𝑩𝑪

𝟕

A

= 𝒙 𝟑𝟓 𝟒𝟎

x

7

?

P Q

𝟑𝟓𝒙 = 𝟐𝟖𝟎

35 40

7-5

𝒙 = 𝟖

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.

𝟕𝟒 𝒚𝒂𝒓𝒅𝒔 PLOT 1 48 yards PLOT 2 Shelby Road PLOT 3 64 yards PLOT 4

B.

C.

𝟒𝟐 𝟐 𝟑 𝟓𝟑 𝟏 𝟑

D. 7

𝟔 𝟒 𝟓 𝒚𝒂𝒓𝒅𝒔 𝒚𝒂𝒓𝒅𝒔 𝒚𝒂𝒓𝒅𝒔

7-5 0% A.

0% B.

0% C.

0% D.

𝑪. 𝟓𝟑 𝟏 𝟑 𝒚𝒂𝒓𝒅𝒔

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 𝑥

PLOT 1 PLOT 2 PLOT 3 PLOT 4

48𝑥 = 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.

𝟏. 𝟗 𝟐. 𝟒

)) )) 12.2

Not drawn to scale.

D.

𝟏𝟑. 𝟓 𝟏𝟏

7-5 0% A.

0% B.

0% C.

0% D.

D.

𝟏𝟏

19. What is the value of x to the nearest tenth?

7-5

4.6

x

5.1

)) )) 12.2

Not drawn to scale.

𝒙 𝟒. 𝟔 = 𝟏𝟐. 𝟐 𝟓. 𝟏 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.

𝟒𝟕. 𝟒 𝒄𝒎; 𝟗. 𝟓 𝒄𝒎

B.

𝟗. 𝟓 𝒄𝒎; 𝟔. 𝟔 𝒄𝒎

C.

𝟑𝟎 𝒄𝒎; 𝟔. 𝟔 𝒄𝒎

D.

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 7.9

= 5 𝑥 or 5 7.9

= 6 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.