Free Printable ILT Similarity Test Review

1.

Given that $\Delta ABC\sim\Delta FED$ , find the value of x.

a)

x = 9

b)

x = 3.9

c)

x = - 0.26

d)

x = 9.95

2.

Which of the following must be true in order for $\Delta BCD\sim\Delta RST$ ?

a)

a = 12 b = 8

b)

a = 24 b = 16

c)

a = 6, b = 4

d)

a = 11, b = 13

3.

Let triangle EFG be a mapped image, dilated about the origin, from triangle JKL with a scale factor k=4 with J(2,2), K(3,4), L(1,0). Which of the following are the coordinates for E?

a)

(12, 16)

b)

(8, 8)

c)

(4, 4)

d)

(4, 0)

4.

Given that $\Delta MNL$ and $\Delta UVL$ are similar, solve for x.

a)

x = -14

b)

x = -9

c)

x = -19.67

d)

x = 7

5.

Given $\Delta ABC$ is a dilated image of $\Delta JKL$ with a scale factor of 4, which of the following proportions are true? Select all that apply.

a)

$\frac{AB}{JK}=\frac{BC}{KL}$

b)

$\frac{AC}{JK}=\frac{BC}{KL}$

c)

$\frac{BC}{KL}=4$

d)

$\frac{KL}{BC}=4$

e)

$\frac{JL}{AC}=\frac{AB}{JK}$

6.

If line segment AB is dilated about center P by a scale factor of ½ to form A’B’, which statement(s) is/are true? Choose all that apply.

a)

AB and A’B’ are parallel.

b)

A’B’ is twice as long as AB.

c)

$\angle ABP\cong\angle BAP$ because they are corresponding angles on parallel lines.

d)

$\frac{AP}{A'P}=\frac{1}{2}$

e)

The endpoints of A’B’ are ½ the distance to P as the endpoints of AB.

7.

Which triangles are similar to triangle A?

a)

B

b)

C

c)

Both

d)

None

8.

Match the following the corresponding sides of the similar figures.

a)

ZW

1.

NK

b)

WX

2.

KL

c)

YZ

3.

MN

d)

XY

4.

LM

9.

Are these two triangles similar? Which similarity criterion do you use to prove it?

a)

Yes, AA Similarity Theorem

b)

Yes, SAS Similarity Theorem

c)

Yes, SSS Similarity Theorem

d)

Not Similar

10.

Find the missing length.

a)

21

b)

18

c)

16

d)

24

11.

Which method can be used to prove the triangles are similar?

a)

AA~

b)

SSS~

c)

SAS~

d)

Not Similar

12.

If two polygons are similar, then the corresponding side lengths are ___________.

a)

congruent

b)

similar

c)

equal

d)

proportional

13.

If two polygons are similar, then the corresponding angles are ___________.

a)

congruent

b)

similar

c)

equal

d)

proportional

14.

Gwen scans a photo that is 4 in. wide by 6 in. tall into her computer. If she scales the height down to 3 in., how wide should the similar photo be?

a)

3 in

b)

2 in.

c)

4 in

d)

1 in

15.

In this figure, triangle TRS is the (a) , triangle T'R'S' is the (b) and a(n) (c) occurred.

Choose from the below words

pre-image

image

enlargement

reduction

spin

flip

16.

Which series of transformations were performed in the figure?

a)

Translation 5 units down, reflection over the y-axis

b)

Reflection over the x-axis, translation 6 units right

c)

Rotation 90^oclockwise, reflection over the x-axis

d)

Rotation 180^oclockwise, reflection over the y-axis

17.

Which of the following are Dilations?

a)

(x, y) → (x, 3y)

b)

(x, y) → (3x, 3y)

c)

(x, y) → (x, y - 3)

d)

(x, y) → (.5x, .4y)

18.

Find the scale factor of the dilation.

19.

State if the triangles in each pair are similar. If so, state how you know they are similar.

a)

Yes, AA Similarity

b)

Yes, SSS Similarity

c)

Yes, SAS Similarity

d)

Not Similar

20.

The triangles are similar, solve for the question mark.

(a)

21.

Complete each proportion.

CB / DM = AC / ?

a)

BM

b)

MA

c)

BC

d)

AD

22.

Complete the similarity statement: $\Delta VUT\sim\Delta$

a)

MVL

b)

VLM

c)

LMV

d)

VML

23.

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?

24.

Solve for the variable x.

25.

Find the missing length indicated.

26.

Find the missing length indicated.

27.

Simplify the radical: √48

28.

Write the similarity statement.

a)

$\Delta RTS\sim\Delta RQP$

b)

$\Delta RTS\sim\Delta RPQ$

c)

$\Delta RTS\sim\Delta QPR$

d)

$\Delta RTS\sim\Delta PQR$

e)

$\Delta RTS\sim\Delta QRP$

29.

In the diagram below of right triangle ABC, WRITE THE SIMILARITY STATEMENT OF ALL 3 TRIANGLES.

a)

$\Delta ABC\sim\Delta CBD\sim\Delta ACD$

b)

$\Delta ABC\sim\Delta CDB\sim\Delta ADC$

c)

$\Delta ABC\cong\Delta CBD\cong\Delta ACD$

d)

$\Delta ABC=\Delta CBD=\Delta ACD$

30.

Name a segment parallel to segment AC

a)

segment DE

b)

segment DB

c)

segment AC

d)

segment BC

31.

Find the missing length indicated.

a)

6

b)

10

c)

5

d)

12

32.

Find x.

a)

6

b)

9

33.

Solve for X

a)

7.5

b)

4.8

c)

13.33

d)

5

34.

Find x.

a)

18

b)

21

c)

11.8

35.

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)

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

36.

Solve for x:

a)

18.6

b)

16.8

c)

22.2

d)

14.2

37.

Solve for x. (HINT: Remember to distribute)

a)

5

b)

10

c)

3

d)

8

38.

Solve for x.

a)

4

b)

9

c)

3

d)

7

39.

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

40.

ΔOBC is similar to ΔOGT because: (choose the best answer)

a)

ΔOBC can be dilated about point O by a scale factor of 1/2, and then rotated 90 degrees about point O.

b)

ΔOBC can be dilated about point G by a scale factor of 1/2, and then reflected over the x- axis

c)

They aren't similar

d)

They map to each other with similarity transformations.

ILT Similarity Test Review

Total questions: 40

Worksheet time: 4hrs 6mins

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