Free Printable Triangle Proportionality/Similarity Applications Review

1.

The Side-Side-Side Similarity (SSS ~) Theorem states if the corresponding sides of two triangles are _____________________, then the triangles are _________________.

a)

proportional; similar

b)

similar, proportional

c)

congruent; congruent

d)

equal; equilateral

2.

The Side-Angle-Side Similarity (SAS ~) Theorem states that if two sides of one triangle are ________________ to two sides of another triangle and their _________________ angles are congruent, then the triangles are similar.

a)

adjacent; intersect

b)

complementary; form

c)

adjacent; create

d)

proportional; included

3.

The Angle-Angle Similarity (AA ~) Theorem states if two angles of one triangle are _______________ to two angles of another triangle, then the triangles are ____________________.

a)

adjacent; equal

b)

complementary; scalene

c)

congruent; similar

d)

supplementary; isosceles

4.

What similarity theorem would you use to prove these triangles are similar?

a)

SAS∼

b)

SSS∼

c)

AA∼

d)

GIF∼

5.

A ~ B. What is the scale factor from A to B?

a)

3/4

b)

2/3

c)

3/2

d)

4/3

6.

Solve the proportion.

a)

p=31.3

b)

p=308

c)

p=924

d)

p=532

7.

Are the triangles similar?

a)

Yes

b)

No

8.

Find the missing length indicated.

a)

30

b)

25

c)

45

d)

50

9.

Find the missing length indicated.

a)

16

b)

8

c)

10

d)

14

10.

Find the value of x

a)

6.75

b)

48

c)

65

d)

53

11.

Find the missing length indicated.

a)

28

b)

8

c)

20

d)

14

12.

Find the value of x

a)

5.6

b)

18

c)

35

d)

25

13.

Find the missing length indicated.

a)

6

b)

10

c)

5

d)

12

14.

Find the missing length.

a)

4

b)

10

c)

8

d)

12

15.

Find the missing length.

a)

35

b)

28

c)

42

d)

13

16.

Which proportion could be used to solve for x?

a)

$\frac{42}{28}=\frac{10x+2}{76}$

b)

$\frac{10x+2}{42}=\frac{48}{28}$

c)

$\frac{28}{42}=\frac{10x+2}{48}$

d)

$\frac{10x+2}{28}=\frac{42}{76}$

17.

Which proportion could NOT be used to find the length of the indicated side?

a)

$\frac{x}{25}=\frac{108-x}{35}$

b)

$\frac{x}{25}=\frac{108}{60}$

c)

$\frac{25}{x}=\frac{35}{108}$

d)

$\frac{25}{35}=\frac{x}{108-x}$

18.

Solve for x

a)

2.05

b)

21

c)

17

d)

-32

19.

Solve for x

a)

1

b)

-2

c)

-8

d)

8

20.

Find the missing length indicated.

a)

42

b)

11

c)

21

d)

30

21.

Find the missing length indicated.

a)

5

b)

12

c)

14

d)

7

22.

Solve for x.

a)

7

b)

14

c)

10

d)

5

23.

Find the value of x.

a)

6

b)

12

c)

8

d)

None of these

24.

Find the value of x.

a)

10

b)

35

c)

8

d)

None of these

25.

What is the value of the missing segment?

a)

462

b)

300

c)

352

d)

256

26.

What is the value of the missing segment?

a)

15

b)

20

c)

6

d)

16

27.

Solve for x.

a)

7

b)

11

c)

3

d)

8

28.

Find the value of x.

a)

6.92

b)

18.67

c)

2.625

d)

13.71

29.

What segment is parallel to EF?

a)

Segment PM

b)

Segment MN

c)

Segment NP

d)

Segment FG

30.

Find the missing length.

a)

6

b)

8

c)

5

d)

None of these

31.

What is the measure of x?

a)

12

b)

15

c)

6

d)

9

32.

Complete each proportion.
CB / DM = AC / ?

a)

BM

b)

MA

c)

BC

d)

AD

33.

Find x.

(a)

34.

Find the value of x.

(a)

35.

Find the value of x.

(a)

36.

Find the value of x.

(a)

37.

Find the value of x.

(a)

38.

Solve for r:

a)

40

b)

60

c)

66

d)

10

39.

What is the length of DB, when Line segment DE is Parallel to line segment BC?

a)

24

b)

32

c)

48

d)

15

40.

Find the length of DE in the figure when you know BC=12, AD=4, DB=2

a)

18

b)

12

c)

8

d)

10

41.

If the line segment XY is parallel to the line segment BC, find the values of p and q .

a)

q=24

p=26

b)

q=32/3

p=36/5

c)

q=32/5

p=36/5

d)

q=18

p=24

42.

Find the length of DF.

a)

8

b)

16

c)

24

d)

32

43.

Find the height of the tree.

a)

8 ft

b)

12 ft

c)

13 ft

d)

15 ft

44.

A telephone booth that is 8 ft tall casts a shadow that is 4 ft long. Find the height of a lawn ornament that casts a 2 ft shadow.

a)

4 ft

b)

2 ft

c)

8 ft

d)

6ft

45.

If a 42.9 ft tall statue casts a 253.1 ft long shadow then how long is the shadow that a 6.2 ft tall man casts?

a)

41.7 ft

b)

36.6 ft

c)

34.6 ft

d)

38.8 ft

46.

A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. How tall is the building?

a)

9 m

b)

15.2 m

c)

12 m

d)

17.5 m

47.

What is the measure of x?

a)

12

b)

15

c)

6

d)

9

48.

To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. What is AB to the nearest meter?

a)

10

b)

12

c)

15

d)

18

49.

A gymnasium is 96 feet long and 75 feet wide. On a blueprint, the gymnasium is 5.5 inches long. To the nearest tenth of an inch, what is the width of the gymnasium on the blueprint?

a)

4.3

b)

8.6

c)

6.4

50.

a)

5

b)

10

c)

12

d)

15

51.

a)

20

b)

30

c)

25

d)

23

52.

To find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. How tall is the tree?

a)

144 feet

b)

72 feet

c)

36 feet

53.

a)

15

b)

13

c)

11

d)

17

54.

a)

8

b)

9.5

c)

10

d)

10.5

55.

A tree casts a shadow that is 12 meters long. At the same time, a 2-meter tall person standing nearby casts a shadow that is 1.5 meters long. How tall is the tree?

a)

14

b)

8

c)

10

d)

16

56.

A flagpole casts a shadow that is 15 meters long. At the same time, a 3-meter tall person standing nearby casts a shadow that is 2 meters long. How tall is the flagpole?

a)

22.5

b)

18

c)

12

d)

10

57.

A ladder is leaning against a wall. The ladder is 5 meters long and the base of the ladder is 3 meters away from the wall. How high up the wall does the ladder reach?

a)

4 meters

b)

2 meters

c)

10 meters

d)

6 meters

58.

A building casts a shadow that is 30 meters long. At the same time, a 2-meter tall person standing nearby casts a shadow that is 1.5 meters long. How tall is the building?

a)

35

b)

25

c)

20

d)

40

59.

A tree casts a shadow that is 20 meters long. At the same time, a 4-meter tall person standing nearby casts a shadow that is 3 meters long. How tall is the tree?

a)

26.67

b)

16.67

c)

30

d)

10

60.

A flagpole casts a shadow that is 10 meters long. At the same time, a 2-meter tall person standing nearby casts a shadow that is 1 meter long. How tall is the flagpole?

a)

5

b)

15

c)

20

d)

25

61.

A ladder is leaning against a wall. The ladder is 8 meters long and the base of the ladder is 6 meters away from the wall. How high up the wall does the ladder reach?

a)

10 meters

b)

6 meters

c)

2 meters

d)

4 meters

62.

A building casts a shadow that is 40 meters long. At the same time, a 5-meter tall person standing nearby casts a shadow that is 2.5 meters long. How tall is the building?

a)

80

b)

100

c)

20

d)

60

63.

Use the information in the diagram to determine the height of the tree.

a)

80 feet

b)

320 feet

c)

40 feet

d)

160 feet

64.

a)

74

b)

100

c)

104

d)

108

65.

A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building? (Draw a picture, set up a proportion)

a)

24 feet

b)

21 feet

c)

27 feet

d)

32 feet

66.

A map has a scale of 3 cm = 18km. If Oakdale and Woodridge are 54 km apart, then they are how far apart on the map?

a)

15 cm

b)

8.7 cm

c)

9 cm

d)

6 cm

67.

At a certain time of day, a 6 ft man casts a 4 ft shadow. At the same time of day, how tall is a tree that casts an 18 ft shadow?

a)

27 ft

b)

1.3 ft

c)

12 ft

d)

16 ft

68.

3. Sunrise Road is 42 miles long between the edge of Moon Lake and Lake Road and 15 miles long between Lake Road and Sunset Road. Lake Road is 29 miles long. Find the length of Moon Lake.

a)

7.63 miles

b)

110.2 miles

c)

81.2 miles

d)

29.48 miles

69.

You need to another support bracket under the ramp in order to make it safe. It must be located 1.5 meters from the end of the 3.6 meter end support. How long should you make your support bracket?

a)

3.6 meters

b)

4.32 meters

c)

4 meters

d)

3 meters

70.

While vacationing in Egypt, the awesome Geometry student Spencer calculated the height of the Great Pyramid. According to Columbus East High School legend, Spencer placed a pole at the tip of the pyramid’s shadow and used similar triangles to calculate its height. This involved some estimating because he was unable to measure the distance from directly beneath the height of the pyramid to the tip of the shadow. Calculate the height of the pyramid from the information given in the diagram.

a)

62.8 meters

b)

155 meters

c)

148.8 meters

d)

258 meters

71.

Find the height of the actual tent:

a)

12 ft.

b)

14.75 ft.

c)

14 ft.

d)

10 ft.

72.

Review the picture. Find the missing side measurement in the picture using a proportion.

a)

x = 900 m

b)

x = 52 m

c)

x = 25 m

d)

x = 0.04 m

73.

Solve for x.

a)

8

b)

6

c)

5

d)

-8

74.

Solve for x

a)

20.8

b)

63.7

c)

27.3

d)

21.4

75.

Do the following side lengths form a triangle?
2 inches, 2 inches, 4 inches

a)

Yes

b)

No

76.

Can the following side measures form a triangle?
4 cm, 7 cm, 10 cm

a)

Yes

b)

No

77.

9. Which of these lengths CANNOT represent the sides of a triangle?

a)

32, 34, 60

b)

28, 30, 58

c)

13, 20, 27

d)

2, 4, 5

78.

In triangle ABC, the length of side AB is 10 inches and the length of side BC is 17 inches. Which of the following could be the length of side AC?

a)

16 inches

b)

5 inches

c)

32 inches

d)

29 inches

79.

Identify the longest side measure.

a)

AC

b)

BA

c)

BC

80.

Identify the smallest angle.

a)

∠A

b)

∠B

c)

∠C

81.

List the angles in order by measure, smallest to largest.

a)

∠B, ∠A, ∠C

b)

∠A∠,B, ∠C

c)

∠A, ∠C, ∠B

82.

Name the angles from LARGEST to SMALLEST

a)

R, S, T

b)

S, T, R

c)

S, R, T

d)

T, S, R

83.

Can a triangle be formed with side lengths:
4, 7, 10

a)

yes

b)

no

c)

not enough information

84.

Can a triangle be formed with side lengths:
17, 9, 30

a)

yes

b)

no

c)

not enough information

Triangle Proportionality/Similarity Applications Review

Total questions: 84

Worksheet time: 2hrs 1mins

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