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WorksheetsTopic 10 Dilations and Similarity Practice
Total questions: 105
Worksheet time: 6hrs 6mins
Name
Class
Date
1.
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(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)
2.
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)
3.
Choose the correct scale factor:
a)
2
b)
3
c)
1/3
d)
1/2
4.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
5.
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)
6.
Dilate Point B by a scale factor of 3:
a)
(12,0)
b)
(12,12)
c)
(4,3)
d)
(0,12)
7.
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
8.
Does the image show a dilation?
a)
Yes
b)
No
9.
A dilation can produce a larger figure or a(n)______
use a synonym for larger
use a synonym for larger
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
10.
A dilation can produce a smaller figure or a(n)______
use a synonym for smaller
use a synonym for smaller
a)
reduction
b)
enlargement
c)
scale factor
d)
center of dilation
11.
A dilation produces a similar figure
a)
True
b)
False
12.
Which of the following transformations will result in an image that is similar, but not congruent, to its original image?
a)
translation
b)
reflection
c)
rotation
d)
dilation
13.
All corresponding angles are congruent in similar figures.
a)
True
b)
False
14.
All corresponding sides are proportional (same ratio) in similar figures.
a)
True
b)
False
15.
In a dilation what mathematical operation is used with the scale factor?
a)
addition
b)
subtraction
c)
multiplication
d)
division
16.
The point (8, 12) was dilated to become point (2, 3). What was the scale factor?
a)
½
b)
¼
c)
4
d)
2
17.
A scale factor of less than one means
a)
that the image will be larger than the pre-image.
b)
That the image will be the same as the pre-image.
c)
That you need to subtract that amount off of each side.
d)
That the image will be a reduction of the pre-image.
18.
What is the scale factor if the triangle on the right is the new triangle?
a)
1/2
b)
7/3
c)
2
d)
10/3
19.
Definition: The figure before a transformation has occurred.
a)
Pre-image
b)
Image
c)
Translation
d)
Reflection
20.
Definition: The figure after a transformation has occurred.
a)
Pre-image
b)
Image
c)
Translation
d)
Reflection
21.
Review the picture. Find the missing side measurement in the picture using a proportion.
a)
w = 18 m
b)
w = 6 m
c)
6 m
d)
w = 0.16 m
22.
What is the similarity statement for the triangle pair?
a)
ΔXYZ~ΔNEW
b)
ΔXZY~ΔNWE
c)
ΔZYX~ΔENW
d)
ΔYZX~ΔNWE
23.
The two right triangles below are similar. What is x, the missing side length in triangle DEF?
a)
3.75
b)
9.75
c)
10
d)
12
24.
Two objects that are the same shape but not the same size are _______.
a)
Congruent
b)
Vertical
c)
Similar
d)
Complementary
25.
Are the two figures similar?
a)
yes
b)
no
26.
Are the polygons similar? Why or why not?
a)
Yes, the angles are congruent and the sides are proportional
b)
No, the corresponding angles are not equal.
c)
No, the sides are not proportional
27.
Solve the proportion.
a)
k=5
b)
k=3.3333333
c)
k=60
d)
k=90
28.
Are the triangles are similar?
a)
yes
b)
no
c)
sometimes
d)
I don't know
29.
Are the triangles similar?
a)
Yes
b)
No
30.
Are the triangles similar?
a)
Yes
b)
No
31.
If ABCDE ∼ GHJDF, then∠B is congruent to _______
a)
∠H
b)
∠D
c)
∠F
d)
∠J
32.
Which triangle is similar to the above triangle ?
a)
A
b)
B
c)
C
d)
D
33.
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
34.
Find the height of the monument.
a)
20
b)
30
c)
25
d)
23
35.
Find the height of the building.
a)
74
b)
100
c)
104
d)
108
36.
Find the height of the flagpole.
a)
15
b)
13
c)
11
d)
17
37.
Find the value of x.
a)
3
b)
4
c)
5
d)
6
38.
Find the value of h.
a)
6.25
b)
5.5
c)
6
d)
5.75
39.
Find the value of d.
a)
8
b)
9.5
c)
10
d)
10.5
40.
Solve the equation for x:
a)
17
b)
16
c)
15
d)
14
41.
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.
42.
Triangle SQR is similar to triangle SPT. Which segment corresponds to segment QR?
a)
A) SP
b)
B) ST
c)
C) PR
d)
D) PT
43.
Why are the triangles similar?
a)
AA~
b)
SAS~
c)
SSS~
d)
AAS~
44.
What is the similarity statement for the triangle pair?
a)
ΔXYZ~ΔNEW
b)
ΔXZY~ΔNWE
c)
ΔZYX~ΔENW
d)
ΔYZX~ΔNWE
45.
Why are the triangles similar?
a)
AA~
b)
ASA~
c)
SAS~
d)
SSS~
46.
Find length of segment AB.
a)
x = 810
b)
x = 21.6
c)
x = 33.75
d)
x = 67.5
47.
Complete the proportion.
AB / BM = ? / CD
AB / BM = ? / CD
a)
BC
b)
AC
c)
MD
d)
MC
48.
Solve for x.
a)
x = 5
b)
x = 3
c)
x = 14
d)
x = 1
49.
Solve for x.
a)
x = 2
b)
x = -1
c)
x = 1
d)
x = 5
50.
What is the value of X?
a)
X=4
b)
X=6
c)
X=3
d)
X=2
51.
A gymnasium is 96 feet long and 75 feet wide. On a blueprint, the gymnasium is 5.5 inches long. To the nearest tenth of an inch, what is the width of the gymnasium on the blueprint?
a)
4.3
b)
8.6
c)
6.4
52.
If the triangles are similar, find x
a)
90
b)
60
c)
30
d)
15
53.
Find the value of x.
a)
6.92
b)
18.67
c)
2.625
d)
13.71
54.
Solve for X
a)
7.5
b)
4.8
c)
13.33
d)
5
55.
Solve for DC
a)
1.5
b)
17.1
c)
8.4
d)
3.5
56.
Solve for x.
a)
3
b)
6
c)
8
d)
9
57.
Find x.
a)
54/7
b)
56/3
c)
11
d)
21/2
58.
Find the scale factor from the bigger triangle to the smaller.
a)
3/2
b)
2/3
c)
12/8
d)
8/12
59.
Determine whether the triangles are similar (name the postulate or theorem you used).
a)
SSS similar
b)
AA similar
c)
SAS similar
60.
Does the image show a dilation?
a)
Yes
b)
No
61.
A scale factor of less than one means
a)
that the image will be larger than the pre-image.
b)
That the image will be the same as the pre-image.
c)
That you need to subtract that amount off of each side.
d)
That the image will be a reduction of the pre-image.
62.
What is the value of X?
a)
X=4
b)
X=6
c)
X=3
d)
X=2
63.
Are the triangles similar?
a)
Yes
b)
No
64.
Find x if 73=x9
a)
21
b)
27/7
c)
13
d)
18
65.
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.
66.
Let triangle XYZ be the dilated image of triangle ABC with a scale factor of k = 3. Which of the following is the correct center of dilation?
a)
(0, 0)
b)
(4, 1)
c)
(-5, 5)
d)
(1, 4)
67.
Given triangle ABC is a dilated image of triangle JKL, the pre-image, with a scale factor of 4, which of the following proportions are true? Select all that apply.
a)
JKAB=KLBC
b)
JKAC=KLBC
c)
KLBC=4
d)
BCKL=4
e)
ACJL=JKAB
68.
If two figures are similar, the corresponding sides are ______________.
a)
equal
b)
congruent
c)
proportional
d)
none of these
69.
Complete the proportion.
DMBC=AD?
a)
BC
b)
AC
c)
MD
d)
MC
70.
The pair of figures is similar. Find the missing side.
a)
x = 9
b)
x = 28
c)
x = 7
d)
x = 63
71.
Find y.
a)
144
b)
18
c)
72
d)
12
72.
To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. Find the length of AB to the nearest meter.
a)
10
b)
12
c)
15
d)
18
73.
Jackson makes a scale model of a building in DC. The actual height of the building is 52 feet. Jackson's model used a scale in which 1 inch represents 5 feet. What is the height in inches of his model?
a)
10.2
b)
10.4
c)
12
d)
14
74.
Which proportion is not the same?
a)
a/b=c/d
b)
a/c=b/d
c)
a/d=b/c
d)
b/a=d/c
75.
The triangles are similar, solve for the question mark.
a)
8
b)
12.5
c)
18
d)
24
76.
Complete the following transformation if Triangle ABC is transformed to make similar Triangle DEF.
Translate A to D. Rotate around Point D until D, E, and _____ are co-linear. Dilate by ______ with center D.
a)
Point B, Scale Factor EF/BC
b)
Point B, Scale Factor BC/EF
c)
Point C, Scale Factor EF/BC
d)
Point C, Scale Factor BC/EF
77.
Which of the following are always similar? Select all that apply.
a)
Circles
b)
Segments
c)
Isosceles Triangles
d)
Regular Polygons
e)
Rectangles
78.
What similarity theorem would prove that these triangles are similar?
a)
SAS∼
b)
SSS∼
c)
AA∼
d)
Side Splitter
79.
How do these triangles appear to be similar?
(Hint: Look for non-labeled parts!)
(Hint: Look for non-labeled parts!)
a)
AA
b)
SAS
c)
SSS
d)
Not Similar
80.
Determine whether the triangles are similar.
a)
SSS~
b)
AA~
c)
SAS~
d)
not similar
81.
When you dilate, you ______ x and y by a number.
a)
Multiply
b)
Add
c)
Subtract
d)
Divide
82.
Dilation's are ________ but not congruent.
a)
Similar
b)
Flipped
c)
Rotated
d)
Congruent
83.
Which rule best represents the dilation that was applied to quadrilateral ABCD to create quadrilateral A'B'C'D'?
a)
(x, y) --> (0.4x, 0.4y)
b)
(x, y) --> (x + 3, y + 1.5)
c)
(x, y) --> (2.5x, 2.5y)
d)
(x, y) --> (x - 1.5, y + 3)
84.
A square has a side length of 5 1/2 inches. This square is dilated by a scale factor of 4/5 to create a new square. What is the side length of the new square?
a)
4 4/5 in
b)
4 1/4 in
c)
4 2/5 in
d)
4 3/4 in
85.
Polygon QRST below was dilated by a scale factor of 9/5 to create polygon Q'R'S'T'. What is the distance in centimeters of point R' to point S'?
a)
16 cm
b)
11.7 cm
c)
17.2 cm
d)
8.89 cm
86.
A triangle has vertices A(-5, -4), B(2, 6), C(4, -3). If the rule (x,y) --> (3x, 3y) What are the vertices of the dilated image?
a)
A'(8, 7) B'(-5, -9) C'(-7, 7)
b)
A'(-8, -7) B'(5, 9) C'(7, -7)
c)
A'(15, 12) B'(6, 18) C'(-12, 9)
d)
A'(-15, -12) B'(6, 18) C'(12, -9)
87.
A triangle has vertices A(0,2), B(4,0), and C(3, -2). Write an algebraic representation for the triangle after a dilation with a scale factor of 2.
a)
(x, y) --> (2x, 2y)
b)
(x, y) --> (x + 2, y + 2)
c)
(x, y) --> (x, y)
d)
(x, y) --> (x - 4, y - 4)
88.
What is NOT one of the critical attributes for similarity?
a)
Same shape, but different size
b)
Congruent angles
c)
Proportional Sides
d)
Sides grow by a common difference
89.
The pair of figures is similar. Find the missing side.
a)
x = 9
b)
x = 28
c)
x = 7
d)
x = 63
90.
If the triangles are similar, find x
a)
4
b)
60
c)
30
d)
16
91.
If the triangles are similar, find y
a)
4
b)
60
c)
30
d)
16
92.
Complete each proportion.
AB / AM = ? / DM
AB / AM = ? / DM
a)
BC
b)
AC
c)
MD
d)
MC
93.
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
94.
What is the value of X and Y ?
a)
X=2.5 and Y=6.5
b)
X=6.5 and Y=2.5
c)
X=3 and Y=7
d)
X=2 and Y= 5
95.
Find AE
a)
12.5
b)
18
c)
11.75
d)
13
96.
Use the information in the diagram to determine the height of the tree.
a)
80 feet
b)
320 feet
c)
40 feet
d)
160 feet
97.
Find the perimeter of the large triangle.
a)
24
b)
36
c)
12
d)
54
98.
Which angle corresponds with ∠X?
a)
∠N
b)
∠W
c)
∠E
d)
∠Y
99.
Which sides corresponds to ZY on triangle WEN?
a)
WE
b)
WN
c)
EW
d)
NE
100.
To measure the distance across a pond, a surveyor locates points A, B, C, D, and E as shown. Find the length of AB to the nearest meter.
a)
10
b)
12
c)
15
d)
18
101.
Jackson makes a scale model of Cade. The actual height of Cade is 52 feet. Jackson's model used a scale in which 1 inch represents 5 feet. What is the height in inches of his model?
a)
10.2
b)
10.4
c)
12
d)
14
102.
On a blueprint of the whitehouse, 0.2 inches represents 5 feet. On the blueprint, what is the length of a room with an actual length of 25 feet?
a)
1 inch
b)
5 inches
c)
0.04 inches
d)
0.4 inches
103.
Which proportion is not the same?
a)
a/b=c/d
b)
a/c=b/d
c)
a/d=b/c
d)
b/a=d/c
104.
A scale factor of 1.4 is applied to shape, what is the change in perimeter?
a)
1.4
b)
1.96
c)
2.8
d)
not enough information
105.
A scale factor of 1.4 is applied to shape, what is the change in area?
a)
1.4
b)
1.96
c)
2.8
d)
not enough information
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