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Worksheets

Transformations, Congruence, and Similarity

Total questions: 70

Worksheet time: 1hrs 13mins

Name
Class
Date
1.
The triangles are similar, solve for the question mark.
a)
8
b)
12.5
c)
18
d)
24
2.
Are the triangles similar?
a)
Yes
b)
No
3.
What similarity theorem would prove that these triangles are similar?
a)
SAS∼
b)
SSS∼
c)
AA∼
d)
Side Splitter
4.
How are the triangles similar?
a)
AA
b)
SAS
c)
SSS
d)
NEI or Not Similar
5.
Given: PQ || BC.  Find the length of AB.
a)
14
b)
11
c)
16
d)
18
6.
Solve for X
a)
7.5
b)
4.8
c)
13.33
d)
5
7.
Solve for x.
a)
8
b)
6
c)
5
d)
-8
8.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
9.
Name the series of transformations that maps ABC onto DEF
a)
reflect over x then translate left 6 up 1
b)
reflect over y then translate down 6 left 1
c)
translate right 6 down 1, then reflect over x
d)
rotate 90 clockwise then reflect over y
10.
Which of the following is NOT true about similar figures?
a)
A) Similar figures always have the same shape.
b)
B) Similar figures always have the same size.
c)
C) Similar figures always have corresponding angles that are equal.
d)
D) Similar figures always have corresponding sides that are proportional.
11.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
12.
If two figures are similar their angles are______.
a)
proportional
b)
congruent
c)
supplementary
d)
complementary
13.

Calculate the value of the scale factor between the 2 triangles

a)

2.5

b)

3

c)

3.5

d)

4

14.
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 or a reduction
15.
The __________ is the ratio of a length of the new figure to the corresponding length on the original figure.
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
16.
Similar figures have the same ______ but different ______. 
a)
measure; shapes
b)
sizes; shapes
c)
value; measures
d)
shape; sizes
17.

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)

18.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
19.
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)
20.
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.
21.

Tell whether the two figures are congruent or similar.

a)

Congruent, because their sides are the same.

b)

Congruent, because their sides are proportional.

c)

Similar, because their sides are the same.

d)

Similar, because their sides are proportional.

e)

They are not congruent or similar.

22.
What is the scale factor from ABCD to MNOP?
a)
2/3
b)
3/2
c)
2
d)
3
23.
The pair of figures is similar. Find the missing side.
a)
x = 9
b)
x = 28
c)
x = 7
d)
x = 63
24.
Which answer shows a reflection across the y-axis?
a)
a
b)
b
c)
c
d)
d
25.

A transformation that “turns” a figure about a point at a given angle and a given direction.

a)

rotation

b)

translation

c)

reflection

d)

dilation

26.

What is the Value of angle A?

a)

∠A=82°

b)

∠A=98°

c)

∠A=180°

d)

∠A=8°

27.

What is the value of angle D?

a)

∠D=116°

b)

∠D=64°

c)

∠D=180°

d)

∠D=26°

28.

What is the value of angle M?

a)

∠M=47°

b)

∠M=133°

c)

∠M=180°

d)

∠M=33°

29.

If angle P measures 60 degrees, what is the measure of angle Q?

a)

60 degrees

b)

30 degrees

c)

120 degrees

30.
Are these triangles congruent?
a)
Yes, by ASA
b)
Yes, by SAS
c)
Yes, by AAS
d)
No, this is the SSA one!!
31.
Are these triangles congruent?
a)
Yes, by AAS
b)
Yes, by SAS
c)
Yes, by ASA
d)
No, this is the SSA one!!
32.
Which is NOT a test to prove triangles congruent?
a)
SAA
b)
SSS
c)
SSA
d)
SAS
33.

Find the value of x.

a)

4

b)

1

c)

-5

d)

-1/2

34.

What is the correct values for x and y?

a)

x = 40, y = 35

b)

x = 35, y = 40

c)

x = 12, y = 30

d)

x = 30, y = 15

35.

Identify the correct picture which represents a 90o clockwise rotation about the origin.

a)
b)
c)
d)
36.
What symbol is used to show that two things are congruent?
a)
≠
b)
≅
c)
≡
d)
=
37.
a)
x = 54
b)
x = 9
c)
x = 24
d)
x = 144
38.

Find the measure of the indicated angle.

a)

120 degrees

b)

40 degrees

c)

20 degrees

d)

60 degrees

39.

Which graph best describes a shape that is reflected over the x - axis?

a)
b)
c)
d)
40.

Are the figures congruent?

(What type of transformation is shown?)

a)

Congruent (rotation)

b)

Congruent (reflection)

c)

NOT Congruent (rotation)

d)

NOT Congruent (reflection)

41.

What is this picture an example of?

a)

Reflection

b)

Translation

c)

Rotation

d)

Dilation

42.
a)

60 degrees

b)

70 degrees

c)

80 degrees

d)

90 degrees

43.

Find the degree measure of ?

a)

21 degrees

b)

31 degrees

c)

49 degrees

d)

59 degrees

44.

Find the degree measure of x

a)

60 degrees

b)

90 degrees

c)

120 degrees

d)

180 degrees

45.

What is the relationship of angles 2 & 3?

a)

Alternate Interior Angles are Congruent

b)

Alternate Exterior Angles are Congruent

c)

Vertical Angles are Congruent

d)

Translated Angles are Congruent

46.

What is the relationship of angle 3 & 5?

a)

Translated Angles are Congruent

b)

Adjacent Angles are Supplementary

c)

Linear Pairs are Supplementary

d)

Consecutive Interior Angles are Supplementary

47.

When two shapes have different side lengths and angles, they are...

a)

congruent

b)

similar

c)

neither congruent or similar

d)

corresponding

48.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
49.

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

50.
What Transformation is visible?
a)
Dilation
b)
Refection
c)
Translation
d)
Rotation
51.
Determine how to translate triangle ABC to triangle A'B'C'. 
a)
right 2, down 5
b)
right 2, down 9
c)
left 2, up 9
d)
left 2, down 9
52.
What is the angle of rotation for this counterclockwise rotation about the origin?
a)
90°
b)
180°
c)
270°
d)
360°
53.

Which sequence of transformations will result from shape F to its image shape F''?

a)

Reflection over both axes

b)

Reflection, then rotation

c)

Translation, then reflection

d)

Rotation, then translation

54.

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 90o clockwise, reflection over the x-axis

d)

Rotation 180o clockwise, reflection over the y-axis

55.
Describe a sequence of transformations that maps figure A onto figure B.
a)
A translation 4 units right followed by a reflection across the x-axis
b)
A reflection across the x-axis followed by a reflection across the y-axis
c)
A reflection across the y-axis followed by a translation 6 units down
d)
A 90° counter-clockwise rotation about the Origin followed by a reflection across the y-axis
56.
How do you write the algebraic notation when the scale factor is 3?
a)
(x, y) goes to (1/3x, 1/3y)
b)
(x, y) goes to (-3x, -3y)
c)
(x, y) goes to (x + 3, y + 3)
d)
(x, y) goes to (3x, 3y)
57.
Which transformation is NOT a rigid motion (the size changes)?
a)
reflection
b)
rotation
c)
dilation
d)
translation
58.

Which shows a dilation?

a)
b)
c)
d)
59.
a)
A
b)
B
c)
C
d)
D
60.
a)
A
b)
B
c)
C
d)
D
61.
a)
A
b)
B
c)
C
d)
D
62.
a)
A
b)
B
c)
C
d)
D
63.
a)
A
b)
B
c)
C
d)
D
64.
a)
A
b)
B
c)
C
d)
D
65.
a)
A
b)
B
c)
C
d)
D
66.
Which triangle congruence theorem can be used to prove the triangles are congruent?
a)
SSS
b)
ASA
c)
AAS
d)
SAS
67.
Which triangle congruence theorem can be used to prove the triangles are congruent?
a)
HL
b)
SSA
c)
SAS
d)
AAS
68.
Which triangle congruence theorem can be used to prove the triangles are congruent?
a)
ASA
b)
SAS
c)
AAS
d)
Not enough information
69.
Which of the following is NOT a triangle congruence theorem?
a)
HL
b)
SAS
c)
AAS
d)
AAA
70.
Which triangle congruence theorem can be used to prove the triangles are congruent?
a)
AAS
b)
ASA
c)
SSA
d)
AAA

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