1. Finding Unknown Lengths in Similar Figures
Course 2
Using Similar Figures
Finding Unknown Lengths in Similar Figures AC QS = AB QR
Write a proportion using corresponding sides. 12 48 14 w =
Substitute lengths of the sides.
12 · w = 48 · 14
Find the cross product.
12w = 672
Multiply.
12w 12
672 12 =
Divide each side by 12 to isolate the variable.
w = 56
QR is 56 centimeters.

2. Insert Lesson Title Here
Course 2
Using Similar Figures
Insert Lesson Title Here
Find the unknown length x
10 cm Q R A B
12 cm
24 cm D C S T AC QS AB QR =
Write a proportion using corresponding sides. 12 24 10 x =
Substitute lengths of the sides.
12 · x = 24 · 10
Find the cross product.
12x = 240
Multiply.
12x 12
240 12 =
Divide each side by 12 to isolate the variable.
x = 20
QR is 20 centimeters.

3. Measurement Application
Course 2
Using Similar Figures
Measurement Application
A volleyball court is a rectangle that is similar in shape to an Olympic-sized swimming pool. Find the length of the pool.
Let l = the length of the pool. 9 25 18 l
Write a proportion using corresponding
side widths. =
9 ·l = 18 · 25
Find the cross products.
9l = 450
Multiply. 9l 9 =
450 9
Divide each side by 9 to isolate the
variable.
l = 50
The pool is 50 meters long.

4. Insert Lesson Title Here
Course 2
Using Similar Figures
Insert Lesson Title Here
The rectangle on the left is similar in shape to the rectangle on the right. Find the width of the right rectangle.
12 cm
6 cm
3 cm ?
Let w = the width of the right rectangle. 6 12 3 w
Write a proportion using corresponding
side lengths. =
6 ·w = 12 · 3
Find the cross products.
6w = 36
Multiply. 6w 6 = 36 6
Divide each side by 6 to isolate the
variable.
w = 6
The right rectangle is 6 cm wide.

5. Using Indirect Measurement
Course 2
Using Similar Figures
Using Indirect Measurement
City officials want to know the height of a traffic signal. The traffic
light casts a shadow that is 45 ft long. A stop sign casts a shadow
that is 30 ft long. If the stop sign is 15 ft high, what is the height of
the traffic light?
Let x = the height of the traffic light. 30 45 15 x =
Write a proportion.
30 · x = 45 · 15
Find the cross product.
30 x = 675
Multiply.
30x 30
675 30
Divide each side by 30 to
isolate the variable. =
x = 22.5
The traffic light is 22.5 feet tall.

6. Insert Lesson Title Here
Course 2
Using Similar Figures
Insert Lesson Title Here
The inside triangle is similar in shape to the outside triangle. Find the length of the base of the inside triangle.
Let x = the base of the inside triangle. 8 2 12 x
Write a proportion using corresponding side
lengths. =
8 · x = 2 · 12
Find the cross products.
8x = 24
Multiply. 8x 8 24 8 =
Divide each side by 8 to isolate the variable.
x = 3
The base of the inside triangle is 3 inches.

7. Insert Lesson Title Here
Course 2
Using Similar Figures
Insert Lesson Title Here
Lesson Quiz
Find the unknown length in each pair of similar figures. J A
3. These two rectangular
cakes are similar in shape. How long is the larger cake?
144 cm 1.
96 cm x
80 cm C K
56 cm B L
84 cm
10 in.
x = 120 cm
6 in. x 2.
9 in.
160 cm
120 cm t
72 cm
90 cm
x = 15 inches
t = 150 cm