Free Printable Review Properties of Similar Figures

1.

All angles in similar figures are congruent.

a)

True

b)

False

2.

Two objects that are the same shape but not the same size are _______.

a)

Congruent

b)

Vertical

c)

Similar

d)

Complementary

3.

Are the following similar? Why or why not?

a)

Yes

b)

No, the corresponding angles are not equal.

c)

No, the ratios of the corresponding sides are not equal.

4.

Tell whether the two figures are similar. Explain your reasoning. (Hint: are they proportional?)

a)

Yes, similar because they are the same shape and side lengths are proportional.

b)

No, not similar because they are the same shape, but side lengths are not proportional.

c)

Yes, same shape

d)

No, different sizes

5.

Are these triangles similar?

a)

Yes

b)

No

6.

Solve for X.

a)

2 ft

b)

3 ft

c)

4 ft

d)

6 ft

7.

Sides in similar figures must be proportional.

a)

True

b)

False

8.

Angles in the same position are called

a)

Corresponding Sides

b)

Corresponding Angles

c)

The Same

d)

Congruent Angles

9.

What is the scale factor if the triangle on the left is the original?

a)

2

b)

3/2

c)

2/3

d)

1/2

10.

True or false, figures that have the same size and the same shape are similar.

a)

True

b)

False

11.

The polygons are similar, but not necessarily drawn to scale. Find the value of x.

a)

x = 8

b)

$x=\frac{11}{2}$

c)

x = 9

d)

x = 10

12.

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

a)

x = 10

b)

x = 4

c)

x = 2

d)

x = 5

13.

Find missing side

a)

5

b)

7

c)

9

d)

11

14.

Solve for f.

a)

6

b)

4

c)

3

d)

8

15.

For the pair of similar figures, find the length of the side marked with a variable.

a)

1.8 in

b)

2.1 in

c)

9.8 in

d)

9.3 in

16.

Triangle ABC is similar to triangle FGH.
What is the value of x in centimeters?

a)

22.5 cm

b)

8 cm

c)

10.8 cm

d)

30 cm

17.

Triangle PQR is similar to triangle XYZ.
What is the length of line segment XZ?

a)

11 in.

b)

13.5 in.

c)

9 in.

d)

20.25 in.

18.

Find the missing side length.

a)

16

b)

12

c)

35

d)

15

19.

Which proportion is true?

a)

$\frac{y}{0.6}=\frac{0.7}{0.56}$

b)

$\frac{y}{x}=\frac{1.25}{1}$

c)

$\frac{x}{1}=\frac{0.5}{1.05}$

d)

$\frac{x}{0.5}=\frac{0.6}{1.25}$

20.

Which proportion is true?

a)

$\frac{v}{w}=\frac{5}{4.38}$

b)

$\frac{v}{6}=\frac{4.2}{2.52}$

c)

$\frac{6}{w}=\frac{5}{7.3}$

d)

$\frac{v}{6}=\frac{7.3}{2.52}$

21.

Select ALL the true statements about an image after a dilation.

a)

The image is a different shape than the preimage.

b)

The image is a different size than the preimage.

c)

The image has the same angle measures as the preimage.

d)

The image is similar to the preimage.

e)

The image has the same side lengths as the preimage.

22.

What side in triangle DEF, corresponds with AB in triangle ABC?

a)

BC

b)

FE

c)

DE

d)

FD

23.

The term "congruent" means ...

a)

matching

b)

similar

c)

corresponding

d)

equal

24.

Figure A′B′C′D′ is the image of figure ABCD under a dilation with the origin as the center and scale

factor $\frac{3}{2}$ . The angle measure of A is ∠36° before the dilation.

What is the measure of angle A’?

a)

72°

b)

54°

c)

36°

d)

18°

25.

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)

26.

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)

27.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

28.

What is the scale factor?

a)

4

b)

.25

c)

5

d)

6

29.

_________ ________ is the number you multiply by the sides to create a similar figure.

a)

Scale Factor

b)

Corresponding Angle

c)

Pi

d)

Mid Point

30.

Which side length corresponds with EF?

a)

ML

b)

LM

c)

OL

d)

EH

31.

Which angle corresponds with angle H?

a)

F

b)

L

c)

E

d)

O

32.

If your SF = 2.5, what type of dilation is it?

a)

Reduction

b)

Enlargement

33.

If your SF = 0.8, what type of dilation is it?

a)

Reduction

b)

Enlargement

34.

What is the formula for scale factor?

a)

$\frac{new}{old}$

b)

$\frac{old}{new}$

35.

a)

0.25

b)

0.5

c)

2

d)

1/2

36.

Which triangle is similar to the above triangle ?

a)

A

b)

B

c)

C

d)

D

37.

What is the scale factor used from A to B?

a)

0.5

b)

3

c)

5

d)

10

38.

What is the scale factor if the triangle on the left is the original?

a)

2

b)

3/2

c)

2/3

d)

1/2

39.

sf = 1/2

a)

Reduction

b)

Enlargement

40.

sf = 5

a)

Reduction

b)

Enlargement

41.

If the scale factor is equal to 1, the copy is ________ the original.

a)

the same as

b)

smaller than

c)

bigger than

42.

These are similar figures. Which proportion can be used to find the missing side?

a)

b)

c)

d)

43.

Which statement is true?

a)

$\angle A\ =\angle E$

b)

$\angle F=\angle B$

c)

$\angle E=\angle B$

d)

$\angle C=\angle D$

44.

$\Delta PQR\ is\ similar\ to\ \Delta STU$ What side corresponds to side UT?

a)

PQ

b)

RQ

c)

QR

d)

QP

45.

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

a)

x = 12

b)

x = 3

c)

x = 40

d)

x = 4

46.

What is the scale factor from the large triangle to the small triangle?

a)

1/2

b)

2/3

c)

3/4

d)

2

47.

Triangle ABC is dilated with a scale factor of 1/2. What is the ordered pair for C’?

a)

C’ (2 , 1)

b)

C’ (-2 , 1)

c)

C’ (2 , -1)

d)

C’ (-2 , -1)

48.

a) If a scale factor of ½ is applied, what would be the algebraic representation for this dilation.

a)

(x, y)--> (2x, 2y)

b)

(x, y)--> (1/2x, 1/2y)

c)

(x, y)--> (x+2, y+2)

d)

(x, y)--> (x-2, y-2)

49.

Solve for x.

a)

21

b)

14

c)

12

d)

18

50.

solve for x

a)

12/11

b)

11/4

c)

4

d)

8

51.

Solve for x

a)

23/13

b)

51/19

c)

7

d)

13

52.

solve for x

a)

3.2

b)

7

c)

69/7

d)

11

53.

solve for x

a)

3

b)

6

c)

41/5

d)

10

54.

solve for x

a)

7.4

b)

10

c)

37/3

d)

16

55.

solve for x

a)

1.5

b)

27/7

c)

9

d)

17.25

56.

solve for x

a)

11

b)

19

c)

31

d)

49

57.

JK is parallel to MN. Solve for y.

a)

5.6

b)

18

c)

35

d)

112.5

58.

Choose the similarity statement for the triangles.

a)

ΔMNL ∼ ΔOPQ

b)

ΔNOM ∼ ΔPQL

c)

ΔLMN ∼ ΔPQO

d)

ΔMLN ∼ ΔPQO

59.

What is the measure of angle F?

a)

36^o

b)

63^o

c)

81^o

d)

99^o

60.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

Review Properties of Similar Figures

Total questions: 60

Worksheet time: 5hrs 42mins

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