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Worksheets

Dilations & Proving Triangles Similar

Total questions: 36

Worksheet time: 3hrs 54mins

Name
Class
Date
1.

Choose the correct scale factor:

(Pay attention to which shape is the preimage!)

a)
2
b)
3
c)
1/3
d)
1/2
2.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
3.
Find the perimeter of the large triangle.
a)
24
b)
36
c)
12
d)
54
4.

What is the definition of similarity?

a)

same shape, same size

b)

same shape, different size

c)

different shape, same size

d)

different shape, different size

5.
How does a dilation change the angles of a polygon?
a)
It changes by the scale factor.
b)
Dilations do not change the angles.
c)
It is impossible to answer this question.  The angles change unpredictably.
d)
The angles all change to larger angles.
6.
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
7.

A scale factor between zero and one means

a)

that the image will be larger than the pre-image.

b)

That the image will be the same as the preimage.

c)
That you need to subtract that amount off  of each side.
d)

That the image will be a reduction of the preimage.

8.
The __________ is the ratio of a length of the image to the corresponding length on the original figure.
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
9.
Are the triangles similar?
a)
Yes
b)
No
10.
Are the triangles similar?
a)
Yes
b)
No
11.

Triangles EFC and CBA are similar. Which sequence of transformations will map one triangle onto the other?

a)

A translation, then a dilation.

b)

A dilation, followed by another dilation.

c)

A reflection, then dilation

d)

A rotation, then a dilation

12.

a)

1//2

b)

1/4

c)

2

d)

4

13.

a)

1/3

b)

3/5

c)

3

d)

10

14.

If a shape goes through the following series of transformations, what do we know about the image?

Rotated 90 degrees clockwise

Dilated by a scale factor of 1.5

Translated 3 units right and 5 units down

a)

The image is CONGRUENT to the pre-image

b)

The image is SIMILAR to the pre-image

15.
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
16.

The two figures are similar. What is the scale factor going from the figure on the left to the figure on the right?

a)

6/5

b)

5/6

c)

25/36

d)

36/25

17.

Challenge: A scale factor of 2 is used to enlarge a square. What is the effect of this change on the AREA of the square?

a)

The area will be half as big.

b)

The area will be twice as large.

c)

The area will be 4 times larger.

d)

The area will be 8 times larger.

e)

The area will not change.

18.

Quadrilateral OBCD is similar to Quadrilateral OHTE because?

a)

Quad OBCD can be reflected over the x axis and then rotated 90 degrees

b)

Quad OBCD can be reflected over the x-axis and then dilated about point O by a scale factor of 2.

c)

Quad OBCD can be reflected over the y-axis and then dilated about the origin by a scale factor of 2.

d)

Quad OBCD can be reflected over the y-axis and then dilated about the origin by a scale factor of 1/2.

19.

Determine if the triangles are similar. If so, state the similarity postulate or theorem.

a)

AA~

b)

SSS~

c)

SAS~

d)

The triangles are not similar.

20.

Which method can be used to show that the two triangles at the right are similar?

a)

AA~

b)

SSS~

c)

SAS~

d)

Cannot be shown

21.

I am allowed to use SSS~ or SAS~ without checking the ratios/proportions of the sides.

a)

True

b)

False

22.

Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA~

b)

SSS~

c)

SAS~

d)

Not similar

23.

Determine if triangles are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)

a)

AA∼AA\sim

b)

SAS∼SAS\sim

c)

SSS∼SSS\sim

d)

The triangles are not similar

24.

Determine if WXZ ~ ZXY. 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 whether the triangles are similar by AA~, SSS~, SAS~, or not similar.

a)

AA~

b)

SSS~

c)

SAS~

d)

NOT SIMILAR

26.

Challenge!

a)

45° : 117° : 18°

b)

50° : 130° : 20°

c)

40° : 104° : 36°

d)

35° : 120° : 22°

27.

Polygon A and B are similar. Give the scale factor of figure A to figure B.

a)

5/2 or 2.5

b)

2/5 or 0.4

c)

5/3

d)

3/5 or 0.6

28.

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

a)

½

b)

¼

c)

4

d)

2

29.
What is the scale factor from ABCD to MNOP?
a)

23\frac{2}{3}

b)

32\frac{3}{2}

c)

2

d)

3

30.

Which algebraic expression could be the rule for a reduction?

a)
(x, y)→(2x, 2y)
b)
(x, y)→(5/2 x, 5/2 y)
c)
(x, y) →(0.5x, 0.5y)
d)
(x, y)→(5x, 5y)
31.

ΔSQR∼ΔSPT. Which choice below lists two corresponding sides?

a)

SP and SR

b)

QS and PT

c)

PS and RS

d)

TP and RQ

32.
a)
ABC and DEF
b)
ABC and GHI
c)
DEF and GHI
d)
None
33.

If the triangles are similar, finish the similarity statement.

If not, choose "not similar"

ΔMLK∼?\Delta MLK\sim?

a)

ΔDEF\Delta DEF  

b)

ΔFED\Delta FED  

c)

ΔEFD\Delta EFD  

d)

not similar

34.

What is Reason #2?

a)

AA ~

b)

SAS ~

c)

SSS ~

d)

Not Enough Information

35.

What is the Reasons for #2 and #3?

a)

#2 - Corresponding Angles Theorem

#3 - AA ~

b)

#2 - Reflexive Property

#3 - AA ~

c)

#2 - Reflexive Property

#3 - SAS ~

d)

#2 - Corresponding Angles Theorem

#3 - SAS ~

36.
What reasons complete the proof?
a)

#2 Given

#3 AA~

b)

#2 Vertical Angles Theorem

#3 AA~

c)

#2 Reflexive Property

#3 SAS~

d)

#2 Definition of Angle Bisector

#2 SSS~

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