Free Printable Geometry: Topic 7 (Similarity)

1.

The pair of figures is similar. Find the missing side.

a)

x = 20

b)

x = 12

c)

x = 5

d)

x = 4

2.

Find the perimeter of the large triangle.

a)

24

b)

36

c)

12

d)

54

3.

Find the height of the person using what you know about similar triangles.

a)

4 ft

b)

6.25 ft

c)

1.25 ft

d)

5.75 ft

4.

What is ratio of any two corresponding sides?

a)

Scale Factor

b)

Corresponding Sides

c)

Similar Figures

5.

All angles in similar figures are congruent.

a)

True

b)

False

6.

If the scale factor is less than one, the new figure will be

a)

an enlargement

b)

a reduction

c)

a scale factor

7.

If the scale factor is greater than one, the new figure will be

a)

a reduction

b)

an enlargement

c)

a scale

d)

not proportional

8.

What is the scale factor from MNOP to ABCD?

a)

2/3

b)

3/2

c)

2

d)

3

9.

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

10.

Find the missing length indicated.

a)

30

b)

25

c)

45

d)

50

11.

The measures of the angles in a triangle are 53⁰,78⁰, and 49⁰. A similar triangle is created by using a dilation with a scale factor of 2. What are the measures of the angles of this triangle?

a)

53⁰,78⁰, and 49⁰

b)

There is not enough information to answer this question.

c)

106⁰,156⁰, and 98⁰

d)

26.5⁰,39⁰, and 24.5⁰

12.

Calculate the value of the scale factor between the 2 triangles

a)

2.5

b)

3

c)

3.5

d)

4

13.

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

a)

B' (2 , 4.5)

b)

B' (-8 ,-18)

c)

B' (8 ,18)

d)

B' (9 ,4)

14.

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

a)

½

b)

¼

c)

4

d)

2

15.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

16.

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?
A(3,3) B(6,6) C(9,3)

a)

A'(9,9) B'(18,18) C'(27,9)

b)

A'(6,6) B'(9,9) C'(12,6)

c)

A'(0,0) B'(3,3) C'(6,0)

d)

A'(1,1) B'(2,2) C'(3,1)

17.

State the coordinate of the image of point B (-10,-6) after a dilation with a scale factor of 1/2.

a)

(5,3)

b)

(20,12)

c)

(-20,-12)

d)

(-5,-3)

18.

Triangle ABC is dilated using a scale factor of 1/2 with the origin as the center of dilation. What are the new coordinates of point A'?

a)

(-3, 3)

b)

(-12, 12)

c)

(-2, 2)

19.

If a triangle has angles measuring 30°, 60°, and 90°, what are the measures of the angles of a triangle similar to it?

a)

30°, 60°, and 90°

b)

60°, 90°, and 30°

c)

There is not enough information to answer this question.

d)

45°, 45°, and 90°

20.

A rectangle is dilated by a scale factor of 3. If the original rectangle had dimensions 2 units by 4 units, what are the dimensions of the dilated rectangle?

a)

6 units by 12 units

b)

5 units by 10 units

c)

6 units by 8 units

d)

3 units by 6 units

21.

Which transformation is NOT a rigid motion (the size changes)?

a)

reflection

b)

rotation

c)

dilation

d)

translation

22.

Definition: The figure before a transformation has occurred.

a)

Pre-image

b)

Image

c)

Translation

d)

Reflection

23.

Definition: The figure after a transformation has occurred.

a)

Pre-image

b)

Image

c)

Translation

d)

Reflection

24.

A dilation always produces a congruent figure.

a)

True

b)

False

25.

A dilation is which of the following:

a)

only an enlargement

b)

only a reduction

c)

either an enlargement or a reduction

d)

neither an enlargement nor a reduction

26.

A dilation always produces a similar figure. Similar figures have the same ______ but different ______.

a)

measure; shapes

b)

sizes; shapes

c)

value; measures

d)

shape; sizes

27.

When the scale factor of a dilation is less than one, the dilation is a...

a)

Reduction

b)

Enlargement

28.

If an image is dilated by a scale factor below, the dilation is a...

k\ =\ \frac{10}{3}

a)

Reduction

b)

Enlargement

29.

State the coordinate of the image of the given point B (-10,-6) under a dilation with center at the origin with the given scale factor k = 1/2.

a)

(5,3)

b)

(20,12)

c)

(-20,-12)

d)

(-5,-3)

30.

Dilate Point B by a scale factor of 1/2

a)

(1.5,-4)

b)

(-1.5,1)

c)

(-1,-1.5)

d)

(-2,-2)

31.

The point (8, 12) was dilated to become point (2, 3). What was the scale factor?

a)

½

b)

¼

c)

4

d)

2

32.

$\frac{AB}{BM\ }=\ \frac{AC}{ }$

a)

CA

b)

MA

c)

DM

d)

CD

33.

Find the missing length indicated. Leave your answer in simplest radical form.

a)

60

b)

100

c)

80

d)

20

34.

Find the missing length indicated. Leave your answer in simplest radical form.

a)

64

b)

12

c)

9

d)

100

35.

a)

10

b)

12

c)

14

d)

16

36.

a)

A

b)

B

c)

C

d)

D

37.

Find the length of the missing side.

a)

17 cm

b)

22 cm

c)

15 cm

d)

13 cm

38.

Solve for m.

a)

-2

b)

2

c)

-9

d)

9

39.

Determine if the triangles are similar. Justify.

a)

Yes, SAS.

b)

Yes, AA.

c)

Yes, SSS.

d)

No, not similar.

40.

a)

A

b)

B

c)

C

d)

D

41.

Find the missing length indicated. Leave your answer in simplest radical form.

a)

b)

100

c)

d)

96

42.

Solve for x and y.

a)

x = 2√26; y = 4√3

b)

x = 2√21; y = 6

c)

x = 2√21; y = 4√3

d)

None of these

43.

In simplest radical form,
√80 is equivalent to

a)

16√5

b)

2√20

c)

4√5

d)

8√5

44.

√28 in simplest radical form:

a)

7√2

b)

7√4

c)

4√7

d)

2√7

45.

Solve for BE

a)

4.5

b)

18

c)

3.6

d)

4

46.

Solve for the variable x.

a)

x = 8.5

b)

x = 10

c)

x = 1

d)

x = 2

47.

Find the missing length.

a)

6

b)

8

c)

5

d)

None of these

48.

Find the missing length.

a)

10

b)

21

c)

35

d)

9

49.

Find the missing length.

a)

25

b)

15

c)

6

d)

16

50.

Solve for the variable x.

a)

x = 8.5

b)

x = 10

c)

x = 1

d)

x = 2

51.

Solve
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

52.

Solve 3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

53.

Find the zeros of the equation:
(x+10)(x-2) = 0

a)

10 and 2

b)

-2 and 10

c)

-10 and 2

d)

-2 and -10

54.

Solve
2x² + 17x + 21 = 0

a)

x= ^-21/₂, -17

b)

x= ²/₃, 16

c)

x=-7, ^-3/₂

d)

x=15, -³/₇

55.

x² + 44 = -15x

a)

{-8, 2}

b)

{-7, 5}

c)

{-11, -4}

d)

{-11}

56.

Find the missing length.

a)

21

b)

18

c)

16

d)

24

57.

Find the missing length.

a)

6

b)

8

c)

5

d)

None of these

58.

Find the missing length.

a)

4

b)

10

c)

8

d)

12

59.

Which proportion would be correct in order to solve for x. (Hint: remember the side splitter theorem states the sides of the triangles are proportional)

a)

x/10 = 15/30

b)

x/10 = 45/30

c)

x/10 = 15/45

d)

x/10 = 30/15

60.

Find the missing length indicated.

a)

8

b)

9

c)

25

d)

12

61.

What is the value of the missing segment?

a)

15

b)

20

c)

6

d)

16

62.

What is the value of the missing segment?

a)

15

b)

20

c)

6

d)

16

63.

What is the value of the missing segment?

a)

12

b)

9

c)

6

d)

16

64.

What is the value of the missing segment?

a)

16

b)

4

c)

12

d)

8

65.

$\frac{AB}{BM\ }=\ \frac{AC}{ }$

a)

CA

b)

MA

c)

DM

d)

CD

66.

Find the missing length indicated.

a)

5

b)

54

c)

3

d)

35

Geometry: Topic 7 (Similarity)

Total questions: 66

Worksheet time: 4hrs 13mins

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