Use this pair of similar triangles to answer part a & b.
Part: A
Which proportion can be used to find AC?
A
AC 11.4

8.4 5.6
B
AC
5.6

8.4 11.4
C
AC
8.4

11.4 5.6
D
AC
5.6

11.4 8.4
Part: B
What is AC?
A
B
C
D
4.1 cm
5.8 cm
7.6 cm
17.1 cm
Mayra wants to find the height of her school building. She stands 40 feet away from the building.
A 5-foot-tall friend stands 8 feet in front of her.
What is the height of Mayra’s school building?
A
20 feet
B
25 feet
C
40 feet
D
64 feet
***The figure below shows two similar rectangles.
What is the length of PQ ?
A
9 cm
B
3 cm
C
4 cm
D
5 cm
ANSWER: B
***The lengths of the sides of one triangle are 8 inches, 10 inches, and 12 inches. What is
the perimeter in inches of a similar triangle whose shortest side is 4 inches?
A
10 inches
B
12 inches
C
15 inches
D
30 inches
ANSWER: C
An artist painted a mural from the photograph shown below.
If the artist used a scale of
1
inch to represent 1 foot, which of the following best
2
represents the dimensions in feet of the mural?
A
4
1
1
ft by 7 ft
2
2
B
1
1
1
ft by 2 ft
2
2
C
6 ft by 10 ft
D
9 ft by 15 ft
ANSWER: C
Alanis is moving and needs to pack two mirrors. The larger mirror fits in a box that is 18 inches wide by
20 inches long. Her smaller mirror is similar in proportion to the larger mirror. Alanis determines that the
width of the smaller box needs to be a minimum of 9 inches. What should be the minimum length of the
box to hold the smaller mirror?
A
2 inches
B
6 inches
C
9 inches
D
10 inches
Which proportion could you use to find the length of RS?
A
5 RS

9
8
B
5 RS

8
9
C
8 RS

5 58
D
9 RS

5
8
ANSWER: D
The accompanying diagram shows two similar triangles.
Which proportion could be used to solve for x?
A
32 15

12 x
B
32 12

x 15
C
x
9

24 15
D
24 15

9
x
In the figure below, ABC is similar to DEF.
What is the length of DF ?
F
4
H
11
G
10
J
16
This is a pair of similar triangles.
Which of the following proportions is true for these triangles?
A
B
C
D
a
s
a
s
a
s
a
s
c
t
b

t
c

r
s

b

In the figure, the two rectangles are similar.
If a = 20, b = 32 and x = 12, what is the value of y?
A
B
C
D
7.5
16
19.2
1
53
3
In graphics class, Ben made two prints of trees on similar sheets of paper.
If the width of the paper used for Tree A is 6 units, what is the height of the paper used for Tree B?
F
7 units
G
10 units
H
11 units
J
12 units
ANSWER: J
What must the value of x be in order for the figures below to be similar?
F
16 cm
G
14 cm
H
12 cm _
J
10 cm
The wooden structure that supports a roller coaster is strengthened by triangular braces as
shown below.
Triangles ACE and BCD are similar triangles and CE = 9 feet, BC = 4 feet, and CD = 4.5
feet. What is the length of AC ?
A
8 feet
B
8.5 feet
C
13 feet
D
13.5 feet
ANSWER: A
7.5C
The two figures shown below are similar.
What is the measure of the missing side?
F
9
G
4
H
3
J
2
In the triangles below, ACE is similar to BCD.
What is the measure of AE ?
A
70 cm
B
60 cm
C
40 cm
D
24 cm
In the diagram below, rectangle JKST and rectangle LRSK are similar.
Which proportion could be used to find the width (x), in feet, of rectangle LRSK?
A
B
C
D
16 6

6
x
16  x 6

6
x
16  x 16

6
x
16 x

6 6
Your soccer team designed pennants in the shape below. The team members decided that
they wanted to make stickers that look like the pennant to boost the spirit of the team. The
company making the stickers needed the missing measurement.
Find the value of x. (Hint: Be sure to change all measurements to inches)
1
A 2
in.
2
B
4 in.
C
1 ft
D
1 ft 1 in.
ANSWER: A
Jake wanted to measure the length, l, of the pond, so he drew this diagram of two similar
triangles.
What is the approximate length, l, of the pond?
A
25 feet
B
19 feet
C
18 feet
D
13 feet
ANSWER: D
If ABC is similar to DEF, which of the following must be true?
A
B
C
D
AB DE

AC
EF
AB
AC

DF
EF
AB DE

BC DF
AB
AC

DE
DF
As shown in the drawing, Raymond used similar triangles to find the height of a pole. When
he stood 6.5 feet from a small puddle, he could see the reflection of the top of the pole in
the puddle. The puddle was 26 feet from the pole, and Raymond’s eye level was 5.5 feet
above the ground.
What is the height of the pole in feet?
A rectangular place mat is similar to the table upon which it is placed.
According to the diagram, which proportion can be used to determine the length of the
table, x?
A
B
C
D
12 24

48
x
12
x

24 48
12 24

x
48
12x = 48
Quadrilateral JKLM is similar to quadrilateral WXYZ.
What is the length of YZ ?
4
in
5
A
4
B
6 in
C
10
D
2
in
3
Not here
ANSWER: A
In the figure below, GH is parallel to JK , so the two triangles are similar.
What is the value of x?
A
4.0
B
5.3
C
9.0
D
10.2
ANSWER: D
Triangles ABC and EFG are similar with measurements in centimeters as shown.
What is the perimeter of triangle EFG?
A
21 cm
B
24 cm
C
36 cm
D
42 cm
Triangle ABC is similar to triangle PQR.
Which proportion can be used to find n?
A
8
n

9 12
B
8
n

12 9
C
4 12

8
n
D
4 12

9
n
What value of x would make ABC similar to DEF?
A
26 _
B
29
C
31
D
32
Which proportion can be used to find the value of PR if XMQ is similar to PRS?
A
B
C
D
20
15
10
5
14
20
15
20
14
PR
7

PR
15

PR
14

PR

The cones below are similar.
What is the radius of cone A?
F
12 units
G
21.3 units
H
24 units
J
27 units
A scout troop marked off similar triangles on the ground in order to find the distance
across a river.
What is the approximate distance across the river?
A
17.1 feet
B
20 feet
C
24 feet
D
28.3 feet
Two similar isosceles triangles are shown below. The dimensions are given in millimeters.
Which statement is TRUE?
F
8 mm
G
8 mm
H
16 mm
J
16 mm
ANSWER: J
7.5C
In the house plan shown below, figure FEB is similar to figure FDA.
What is the length of segment AD?
A
12 feet
B
20 feet
C
30 feet
D
35 feet
ANSWER: B
If XYZ is similar to STU, what is the length of XY XY in centimeters?
A
9 cm
B
10.5 cm
C
12 cm
D
12.5 cm
ANSWER: B
What must the value of x be in order for the figures below to be similar?
A
11 cm
B
23.3 cm
C
20.7 cm
D
13 cm
****ABC is similar to JKL. If the perimeter of ABC is 12 inches, what is the perimeter
of JKL?
A. 8 inches
B. 10 inches
C. 24 inches
D. 36 inches
ANSWER: 24
The parallelogram shown below has sides measuring 20.5 centimeters and 14 centimeters.
Cecilia draws a similar parallelogram so that the longest two sides are each
24.6 centimeters. What is the length of one of the other sides of Cecilia’s parallelogram?
A. 18.1 centimeters
B. 16.8 centimeters
C. 11.7 centimeters
D. 9.9 centimeters
ANSWER: B
Danielle is drawing two similar triangles in the sand. The smaller triangle has side
lengths of 3 feet, 2 feet, and 4 feet. Two corresponding sides of the second triangle
are 6 feet and 4 feet in length. What is the length of the third side of the larger?
triangle?
A
4 feet
B
5 feet
C
6 feet
D
8 feet
1
foot wide photo to make a poster for school. If the poster
2
is 6 feet tall and is similar to the photo, what is the width of the poster?
You enlarged a 4 inch tall by
A
4 ft
B
8 ft
C
9 ft
D
12 ft
The accompanying diagram shows a section of the city of Tacoma. High Road, State Street,
and Main Street are parallel and 5 miles apart. Ridge Road is perpendicular to the three
parallel streets. The distance between the intersection of Ridge Road and State Street and
where the railroad tracks cross State Street is 12 miles. What is the distance between the
intersection of Ridge Road and Main Street and where the railroad tracks cross Main Street?
ANSWER: 24 ft
The cylinders below are similar.
What is the radius of cylinder A?

F
7.35 units
G
11 units
H
22 units
J
24.75 units

The Rivera family bought a new tent for camping. Their old tent had equal sides of 10 feet
and a floor width of 15 feet, as shown in the accompanying diagram.
If the new tent is similar in shape to the old tent and has equal sides of 16 feet, how wide
is the floor of the new tent?
ANSWER: 24 ft
Figures ABCD and EFGH are similar. The ratio of their corresponding sides is 5:1.
What is the length of GH ?
A
3 units
B
4 units
C
5 units
D
10 units
ANSWER: A
In the diagram below, two ladders are placed against the side of a house to form similar
right triangles. The taller ladder reaches 13 feet above the ground, and its base is
8 feet from the house. The base of the shorter ladder is 4 feet from the house.
How far is the top of the shorter ladder from the top of the taller ladder?
F
4.5 feet
G
6.5 feet
H
8 feet
J
9 feet
ANSWER: G
Leah is building a skateboard ramp that is similar to Jay’s skateboard ramp, as shown
below. Jay’s ramp has the following dimensions: length = 18 feet and height = 12 feet.
Leah wants the height of her ramp to be 8 feet. What should the length of Leah’s ramp
be if it is similar to Jay’s ramp?
A
16 ft
B
14 ft
C
12 ft
D
9 ft
Triangle ABC is similar to triangle XYZ.
What is the length of XZ ?
A
5 units
B
6 units
C
8.1 units
D
17.34 units
Myra’s dad is making her a rocking chair similar to the miniature chair shown below.
1
1
inch wide and 1 inches tall. If Myra’s chair is 18 inches
2
2
wide, how tall will it be?
The miniature chair is
A
1.5 feet
B
4.5 feet
C
18 feet
D
54 feet
Parallelogram DEFG is similar to parallelogram VUXW.
What is the length of UX ?
A
21.6 in.
B
8 in.
C
3.75 in.
D
2 in.
OPEN ENDED
An art museum gift shop has rectangular posters that are similar to actual rectangular
paintings. One poster that is 18 inches long is similar to a painting that is 45 inches long
and 30 inches wide.
a. What is the scale factor used to reduce the size of the actual painting to the size of the
poster? Express the scale factor as a fraction in simplest form. Show or explain how you
got your answer.
b. What is the width, in inches, of the poster that is 18 inches long? Show or explain how
you got your answer.
c. All the posters are sized using the same scale factor. A second poster is 16 inches long
and 14 inches wide. What are the dimensions, in inches, of the actual painting? Show or
explain how you got your answer.