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Ratio, Proportion, & Similarity Practice

Total questions: 25

Worksheet time: 40mins

Name
Class
Date
1.

There are 21 boys and 30 girls in the school band. Find the ratio for number of boys in the band to the total number of students in the band.

a)

21 : 51

b)

21 : 30

c)

51 : 21

d)

30 : 21

2.

In a certain apartment building, the ratio of tenants to cars is 3:5. If there are 30 tenants, how many cars are there?

(a)  

3.

In an animal shelter, the ratio of dogs to cats is 5 to 3. There are 25 dogs.  Write and solve a proportion to find the number c of cats.

(a)  

4.

If Justin can type 408 words in 4 minutes, how many words can he type per minute?

(a)  

5.

Solve for a. Round to the nearest tenth.

(a)  

6.

Solve for x. Round to the nearest tenth.

(a)  

7.

Solve the equation for x. Round to the nearest hundredth.

(a)  

8.

Look at the two triangle in the picture. The two triangles are similar. Select the correct similarity statement.

a)

ΔCBA∼ΔPQR\Delta CBA\sim\Delta PQR

b)

ΔABC∼ΔQRP\Delta ABC\sim\Delta QRP

c)

ΔABC∼ΔPQR\Delta ABC\sim\Delta PQR

d)

ΔBCA∼ΔRQP\Delta BCA\sim\Delta RQP

9.

Use the picture to find the missing side length. Select your answer below.

a)

A

b)

B

c)

C

d)

D

10.

Use the picture to find the value of x.

a)

14 ft

b)

28 ft

c)

10 ft

d)

18 ft

11.

ΔPRQ ∼ ΔDEF\Delta PRQ\ \sim\ \Delta DEF  
What is  DEDE  ?

(a)  

12.

These figures are similar. Solve for x.

(a)  

13.

The polygons are similar. Find the value of x.

(a)  

14.

Find the scale factor.

a)

4:1

b)

3:1

c)

2:1

d)

3:2

e)

7:3

15.
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.
16.

Are the triangles similar? If so, what similarity shortcut is used?

a)

Similar. SAS

b)

Similar. AA

c)

Similar. SSS

d)

Not Similar

17.
State the postulate that proves these triangles are similar.
a)
SSS
b)
AA
c)
SAS
d)
Not similar
18.
Choose the similarity statement for the triangles.
a)
ΔMNL ∼ ΔOPQ
b)
ΔNOM ∼ ΔPQL
c)
ΔLMN ∼ ΔPQO
d)
ΔMLN ∼ ΔPQO
19.

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)  

20.
If ABCDE ∼ GHJDF, then∠B is congruent to _______
a)
∠H
b)
∠D
c)
∠F
d)
∠J
21.

Determine if the triangles are similar. If similar, select the correct theorem.

a)

SSS ~

b)

SAS ~

c)

AA ~

d)

Not similar

22.

Determine if the triangles are similar. If similar, select the correct theorem.

a)

SSS ~

b)

SAS ~

c)

AA ~

d)

Not ~

23.

Determine if the triangles are similar. If similar, state the theorem.

a)

SSS ~

b)

SAS ~

c)

AA ~

d)

Not ~

24.

Determine if the triangles are similar. If similar, state the theorem.

a)

SSS ~

b)

SAS ~

c)

AA ~

d)

Not ~

25.

Determine if the triangles are similar. If similar, state the theorem.

a)

SSS ~

b)

SAS ~

c)

AA ~

d)

Not ~