Free Printable Unit 1

1.

A dilation is which of the following:

a)

An enlargement

b)

A reduction

c)

Either an enlargement or a reduction

d)

Neither an enlargement or a reduction

2.

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

a)

an enlargement

b)

a reduction

c)

a scale factor

d)

bigger

3.

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

4.

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)

5.

Dilate Point B by a scale factor of 3:

a)

(12,0)

b)

(12,12)

c)

(4,3)

d)

(0,12)

6.

Which of the following is the algebraic representation for a dilation?

a)

(x, y) → (x, 3y)

b)

(x, y) → (3x, 3y)

c)

(x, y) → (x, y - 3)

d)

(x, y) → (.5x, .4y)

7.

a)

A

b)

B

c)

C

d)

D

8.

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

a)

½

b)

¼

c)

4

d)

2

9.

Choose the correct scale factor:

a)

2

b)

3

c)

1/3

d)

1/2

10.

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)

11.

Choose the correct scale factor:

a)

2.5

b)

1.5

c)

3.5

d)

4

12.

a)

A

b)

B

c)

C

d)

D

13.

What is the scale factor shown in the dilation shown?

a)

5

b)

1/5

c)

10

14.

Figure ABCD has an area of 4 units². It is then dilated using a scale factor of 4. What is the perimeter of the new figure?

a)

32

b)

64

c)

8

15.

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

a)

(-3, 3)

b)

(-12, 12)

c)

(-2, 2)

16.

The "image" is the shape before the dilation.

a)

True

b)

False

17.

If a dilation produces a congruent figure, then the scale factor was equal to _____.

a)

1/2

b)

2

c)

10

d)

1

18.

a)

F

b)

G

c)

H

d)

J

19.

a)

32 inches

b)

64 inches

c)

112 inches

d)

224 inches

20.

Which rule shows the transformation?

a)

(x, y) ----> (0.5x, 0.5y)

b)

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

c)

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

d)

(x, y) -----> (3x, 3y)

21.

A dilation is a transformation of a figure in which the figure stretches or shrinks with respect to a fixed point called the center of the dilation.

(a)

22.

The number that you multiply by to stretch or shrink a figure.

(a)

23.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

24.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

25.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

26.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

27.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

28.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

29.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

30.

Determine if the triangles are similar. If they are, identify the triangle similarity theorem(s) that prove(s) the similarity.

a)

AA ~ Theorem

b)

SAS ~ Theorem

c)

SSS ~ Theorem

d)

Not similar

31.

Complete the similarity statement: △CED ~ _______

a)

△TUV

b)

△VTU

c)

△TVU

d)

△UTV

32.

Complete the similarity statement: △WYX ~ _______

a)

△WYZ

b)

△WZY

c)

△YZW

d)

△YWZ

33.

Complete the similarity statement: △ADB ~ _______

a)

△ACE

b)

△AEC

c)

△EAC

d)

△ECA

34.

Complete the similarity statement: △ACB ~ _______

a)

△HFG

b)

△HGF

c)

△FHG

d)

△FGH

35.

Complete the similarity statement: △ACB ~ _______ ~ _______

a)

△ACD, △ABD

b)

△DCA, △BDA

c)

△ACD, △BDA

d)

△DCA, △DAB

36.

Which two U.S. states don’t observe Daylight Saving Time?

a)

Montana

b)

Hawaii

c)

Alaska

d)

Arizona

37.

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

38.

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

39.

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

40.

Which is not a similar triangle theorem?

a)

ASA∼

b)

SAS∼

c)

SSS∼

d)

AA∼

41.

State the postulate that proves these triangles are similar.

a)

AA~

b)

SAS~

c)

SSS~

d)

AAS~

42.

State the postulate that proves these triangles are similar.

a)

SSS~

b)

SAS~

c)

AA~

d)

Not similar

43.

State the postulate that proves these triangles are similar.

a)

AA~

b)

SAS~

c)

SSS~

d)

Not Similar

44.

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

(a)

45.

) Side-Side-Side Similarity Theorem

If all three corresponding sides of two triangles are proportional, then the triangles are similar.

(a)

46.

3) Side-Angle-Side Similarity Theorem

If two of the corresponding sides of two triangles are proportional and the included angles are congruent, then the triangles are similar.

(a)

47.

Find the height of the tree.

a)

8 ft

b)

12 ft

c)

13 ft

d)

15 ft

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.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

50.

At the same time a 6 foot person casts a 2 foot shadow, a nearby flagpole casts a ten foot shadow. How tall is the flagpole?

a)

3 feet

b)

10 feet

c)

16 feet

d)

30 feet

51.

A tree is 72 feet tall and has a shadow that is 12 feet long. A nearby tree has a shadow of 5 feet. How tall is the tree?

a)

3 ft.

b)

300 ft.

c)

30 ft.

d)

35 ft.

52.

Find missing side

a)

5

b)

7

c)

9

d)

11

53.

Read the problem and find the missing measurement. Use labels or pictures to help set up the problem.
A home's height is 40 ft. and casts a shadow that is 12 ft.. A car in the driveway is 10 ft. high. How long is the car's shadow?

a)

x = 3 ft.

b)

x = 12 ft.

c)

x = 120 ft.

d)

none of the above

54.

Solve for f.

a)

6

b)

4

c)

3

d)

8

55.

a)

5

b)

10

c)

12

d)

15

56.

Find side length X.

a)

30

b)

25

c)

15

d)

40

57.

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

a)

Congruent

b)

Vertical

c)

Similar

d)

Complementary

58.

Matching sides are called

a)

Corresponding Sides

b)

Corresponding Angles

c)

The Same

d)

Congruent Sides

59.

Sides in similar figures must be proportional.

a)

True

b)

False

60.

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

61.

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

62.

The triangles are similar, solve for the question mark.

a)

8

b)

12.5

c)

18

d)

24

63.

A tree is 72 feet tall and has a shadow that is 12 feet long. A nearby tree has a shadow of 5 feet. How tall is the tree?

a)

3 ft.

b)

300 ft.

c)

30 ft.

d)

35 ft.

64.

Find missing side

a)

5

b)

7

c)

9

d)

11

65.

Find side length X.

a)

30

b)

25

c)

15

d)

40

66.

a)

205

b)

105

c)

230

d)

135

67.

A flagpole is 1 in.= 4 ft. If the pole measures 12 inches, how tall is the actual pole?

a)

16 feet

b)

3 feet

c)

48 feet

d)

9 feet

68.

Angle C and P are...

a)

Alternate Interior Angles

b)

Consecutive Interior Angles

c)

Corresponding Angles

d)

Alternate Exterior Angles

69.

a)

15

b)

13

c)

11

d)

17

70.

Find the height of the tree.

a)

8 ft

b)

12 ft

c)

13 ft

d)

15 ft

71.

a)

205

b)

105

c)

230

d)

135

72.

Find the height of the building

a)

74ft

b)

100ft

c)

104ft

d)

108ft

73.

Find the length of the missing side.

a)

26 cm

b)

18 cm

c)

101.4 cm

d)

15 cm

74.

a)

The river is 4.8 m wide.

b)

The river is 30 m wide.

c)

The river is 7.5 m wide.

d)

The river is 32 m wide.

75.

a)

2

b)

7

c)

0.5

d)

12

76.

a)

10 ft

b)

5 ft

c)

8 ft

d)

15 ft

77.

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

78.

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

a)

1.8 in

b)

2.1 in

c)

9.8 in

d)

9.3 in

79.

Cross Multiplying Vocab #7

We can use this to solve for a variable if there’s a fraction equals a fraction.

(a)

80.

Indirect Measure Vocab #8

We can use similar triangles to calculate heights or lengths that are difficult to measure in real life.

(a)

81.

Find the missing length.

a)

10

b)

21

c)

35

d)

9

82.

Find the missing length.

a)

25

b)

15

c)

6

d)

16

83.

Find the missing length.

a)

25

b)

20

c)

21

d)

15

84.

Find the missing length.

a)

8

b)

7

c)

20

d)

40

85.

Find the missing length.

a)

15

b)

11

c)

35

d)

8

86.

Find the missing length.

a)

12

b)

10

c)

16

d)

5

87.

Solve for x.

a)

5

b)

10

c)

3

d)

8

88.

Solve for x.

a)

10

b)

9

c)

6

d)

5

89.

Solve for x.

a)

8

b)

4

c)

7

d)

5

90.

Solve for x.

a)

5

b)

3

c)

8

d)

6

91.

Solve for x.

a)

8

b)

7

c)

5

d)

10

92.

Solve for x.

a)

7

b)

3

c)

9

d)

10

93.

Solve for x.

a)

3

b)

10

c)

9

d)

7

94.

Solve for x.

a)

7

b)

6

c)

10

d)

3

95.

Solve for x.

a)

8

b)

3

c)

6

d)

4

96.

Solve for x.

a)

6

b)

8

c)

9

d)

10

97.

Find the missing length indicated.

Write down your work.

a)

30

b)

25

c)

45

d)

50

98.

Solve for x.

Write down your work.

a)

18

b)

12

c)

6.75

d)

85.3

99.

Find the missing length indicated.

Write down your work.

a)

6

b)

10

c)

5

d)

12

100.

Which proportion could be used to prove that $HJ\parallel KL$ ?

a)

$\frac{KL}{HJ}=\frac{KG}{LG}$

b)

$\frac{KH}{KG}=\frac{LG}{LJ}$

c)

$\frac{HK}{JL}=\frac{LG}{GK}$

d)

$\frac{GK}{HK}=\frac{GL}{LJ}$

101.

Find AB. Hint: Solve for x and then find AB.

Write down your work.

a)

16

b)

4

c)

8

d)

48

102.

Complete each proportion.
AB / BM = ? / CD

a)

BC

b)

AC

c)

MD

d)

MC

103.

Are the triangles similar?

Write down your work.

a)

Yes

b)

No

104.

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

105.

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

a)

Congruent

b)

Vertical

c)

Similar

d)

Complementary

106.

Select the proportion that shows the Triangle Proportionality Theorem.

a)

$\frac{6}{27}=\frac{7}{x}$

b)

$\frac{6}{21}=\frac{7}{x}$

c)

$\frac{7}{6}=\frac{x}{27}$

107.

Which triangles are similar to triangle A?

a)

B

b)

C

c)

Both

d)

None

108.

If two figures are similar, the corresponding sides are ______________.

a)

equal

b)

congruent

c)

proportional

d)

none of these

109.

What is the height of the flag pole?

Show your work.

a)

205

b)

105

c)

230

d)

135

110.

Find the value of x

a)

5.6

b)

18

c)

35

d)

25

111.

What segment is parallel to EF?

a)

Segment PM

b)

Segment MN

c)

Segment NP

d)

Segment FG

112.

QR is a midsegment of triangle WUV. What is the length of segment QR?

a)

4

b)

8

c)

16

d)

32

113.

What is the measure of angle X?

a)

60

b)

40

c)

140

d)

100

114.

What is the measure of angle Y?

a)

60

b)

40

c)

140

d)

100

115.

QR is a midsegment of triangle WXY. What is the length of segment WY?

a)

3

b)

6

c)

9

d)

12

116.

QR is a midsegment of triangle FGH. Solve for the value of x?

a)

5.5

b)

11

c)

-5.5

d)

-11

117.

QR is a midsegment of triangle BCD. Solve for the value of x.

a)

11

b)

18

c)

9

d)

-7

118.

TS is a midsegment of triangle GHI. Solve for the value of x.

a)

4

b)

6

c)

8

d)

10

119.

KJ is a midsegment of WXV. What is the length of segment VX?

a)

6

b)

12

c)

9

d)

-2

120.

IJ is a midsegment of triangle MLN. What is the length of segment IJ?

a)

9

b)

6

c)

18

d)

0

121.

VW is a midsegment of triangle KIJ. What is the length of segment KI?

a)

-1

b)

-10

c)

18

d)

8

122.

UV is a midsegment of triangle FGH. What is the length of segment UV?

a)

12

b)

10

c)

5

d)

-12

123.

Mr. Sparzak and Mr. Shively are...

a)

dumb

b)

triflin'

c)

the worst

d)

my favorite teachers

Unit 1 - Similarity

Total questions: 123

Worksheet time: 5hrs 9mins

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