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Review For Similarity and Congruence Test

Total questions: 50

Worksheet time: 2hrs 24mins

Name
Class
Date
1.
Two objects that are the same shape but not the same size are _______.
a)
Congruent
b)
Vertical
c)
Similar
d)
Complementary 
2.
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
3.
Two objects that are the same shape but not the same size are _______.
a)
Congruent
b)
Vertical
c)
Similar
d)
Complementary 
4.

The triangles are similar. Find missing side

a)

5

b)

7

c)

9

d)

11

5.
Find the perimeter of the large triangle.
a)
24
b)
36
c)
12
d)
54
6.
Find the height of the tree.
a)
8 ft
b)
12 ft
c)
13 ft
d)
15 ft
7.
On a map, the distance between two towns in 2.6 cm. The scale of the map is 1 cm:50 km. What is the actual distance between the two towns?
a)
100 km
b)
130 km
c)
70 km
d)
150 km
8.

A rectangular garden is 45 ft wide and 70 ft long. On a blueprint, the width is 9 in. Identify the length on the blueprint.

a)

350 ft

b)

9 in

c)

12 in

d)

14 in

9.

Are the following similar? Why or why not?

a)

Yes

b)

No, the corresponding angles are not equal.

c)

No, the ratios of the corresponding sides are not equal.

d)

No, they are congruent.

10.

The pair of figures is similar. Find the missing side.

a)

x = 9

b)

x = 63

c)

x = 7

d)

x = 28

11.
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
12.

Are the following similar? Why or why not?

a)

Yes

b)

No, the corresponding angles are not equal.

c)

No, the ratios of the corresponding sides are not equal.

d)

No, they are congruent.

13.

Complete each proportion for the similar triangles.

CB / DM = AC / ?

a)

BM

b)

MA

c)

BC

d)

AD

14.

Find missing side for the similar triangles.

a)

5

b)

7

c)

9

d)

11

15.
The pair of figures is similar. Find the missing side.
a)
x = 9
b)
x = 28
c)
x = 7
d)
x = 63
16.
A blueprint was using a scale of 3cm=4.5m. Find the actual length if it is 5cm on the drawing.
a)
7.5
b)
13.5
c)
1.5
d)
1.7
17.
A scale drawing of a house shows 9cm ×10cm. If 6cm=12 ft, what are the actual dimensions?
a)
9ft x 10ft
b)
1ft x 2ft
c)
12ft x 6ft
d)
18ft x 20ft
18.
If the actual dimensions of the kitchen are 24 ft. by 24 ft., what is the scale of the drawing?
a)
1cm : 9ft
b)
1cm : 8ft
c)
4cm : 1ft
d)
1cm : 4ft
19.
Scale: 1in.=7ft. The actual width of the backyard is 49 ft, how wide is it in the drawing?
a)
14 in 
b)
7 in
c)
42 in
d)
56 in
20.
Tell whether the two figures are similar. Explain your reasoning.
a)
Yes, similar because they are the same shape and side lengths are proportional.
b)
No, not similar because they are the same shape, but side lengths are not proportional.
c)
Yes, same shape
d)
No, different sizes
21.
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
22.
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
23.
The distance between two cities on a map is 4.125 inches.  Find the actual distance if the scale on the map is 2 inches = 40 miles.
a)
165 miles
b)
50 miles
c)
82.5 miles
d)
41.25 miles
24.
Robbie made a scale drawing of a neighborhood park. A soccer field in the park is 14 inches long in the drawing. The actual field is 98 yards long. What is the scale of the drawing?1 inch = _ yards
a)
1372
b)
5
c)
14
d)
7
25.
a)
0.25
b)
0.5
c)
2
d)
1/2
26.

Which triangle could be similar to the above triangle ?

a)

A

b)

B

c)

C

d)

D

27.
On a map, Memphis, Tennessee, and Jackson, Mississippi, are 5 inches apart. The distance between the cities is actually 210 miles.

What scale was used to create the map?
a)
42 inches = 1 mile
b)
1 inch = 42 miles
c)
40 inches = 1 mile
d)

1 inch = 40 miles
28.

The model of a picture has the area of 52 sq. in. What is the area of the actual picture if the scale factor is 3.5:1?

a)

182 inches squared

b)

637 inches squared

c)

104 inches squared

d)

12.25 inches squared

29.
A rectangle has dimensions of 3 x 5 inches. The image is created with a scale factor of 1/2. What is the  area of the image?
a)
.75 square inches
b)
3.75 square inches
c)
60.0 square inches
d)
1.5 square inches
30.
If the length of the pre-image  is 12 units and the scale factor is 1/4 what is the length of the image?
a)
300
b)
4.8
c)
3
d)
4
31.
An architect is drawing a house and decides that 1.5 inches = 2 feet in his drawing. In real life the living room has a length of 17 feet. What is the length of the room  on his blueprint (drawing)?
a)
12.75 inches
b)
15.5 inches
c)
22.67 inches
d)
51 inches
32.

Find the area of a rectangle similar to this rectangle if it is dilated by a scale factor of 4.

a)

160 square feet

b)

640 feet squared

c)

2560 feet squared

d)

1600 feet squared

33.

What is the scale factor?

a)

3

b)

1/3

c)

4

d)

1/4

34.

Answer the following question about the dilation centered at O with a scale factor of 3. OA = 4, OB = 6 and AB = 5.


Find A'B'.

a)

15

b)

1/15

c)

12

d)

18

35.
Pedro and his friends are visiting chocolate shops in Fairview. They take a cab from one chocolate shop to another. On a map, the two are separated by 3 centimeters. If the scale of the map is 1 centimeter = 2 kilometers, then what is the actual distance between the two chocolate shops?
____ = ____
a)
1/2 kilometer 
b)
1.5 kilometers
c)
6 kilometers
d)
3 kilometers
36.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
Not enough information
37.
Name the postulate, if possible, that makes the triangles congruent.
a)
SAS
b)
ASA
c)
AAS
d)
Not enough information
38.

Name the postulate, if possible, that makes the triangles congruent.

a)

HA

b)

LA

c)

HL

d)

Not enough information to prove congruence.

39.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
ASA
c)
AAS
d)
Not enough information
40.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
AAS
d)
Not enough information
41.
Name the postulate, if possible, that makes the triangles congruent.
a)
SAS
b)
ASA
c)
AAS
d)
Not enough information
42.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
AAS
43.

Name the postulate, if possible, that makes the triangles congruent.

a)

HL

b)

HA

c)

LA

d)

Not enough information

44.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
AAS
d)
Not enough information
45.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
Not enough information
46.
Name the postulate, if possible, that makes the triangles congruent.
a)
SSS
b)
SAS
c)
ASA
d)
AAS
47.
Choose the correct congruence statement.
a)
A
b)
B
c)
C
d)
D
48.
Choose the correct item to make the congruence statement true.
a)
A
b)
B
c)
C
d)
D
49.
What other piece of information is needed to prove the triangles congruent by SSS?
a)
A
b)
B
c)
C
d)
D
50.

Which transformation does not result in congruent figures?

a)

translation

b)

dilation

c)

relfection

d)

rotation

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