1. Similar figures have the same shape but not necessarily the same size.
Corresponding angles are the same
Corresponding sides are proportional
Corresponding means in the same relative position on the figure
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

2. Additional Example 1: Finding Unknown Lengths in Similar Figures
Find the unknown measures in the similar figures. H B
10 cm
31° A y
58 cm x
6 cm
116 cm
59° J G C
5 cm AB JG = BC HG
Write a proportion using corresponding sides. 10 5 6 x =
Substitute lengths of the sides.
10 · x = 5 · 6
Find the cross product.
10x = 30
Multiply.
10x 10 30 10 =
Divide each side by 12 to isolate the variable.
x = 3
HG is 3 centimeters.

3. Additional Example 1 Continued
Find the unknown measures in the similar figures. H B
10 cm
31° A y
58 cm x
6 cm
116 cm
59° J G C
5 cm
Step 2 Find y.
Corresponding angles of similar
triangles have equal angle
measures.
H corresponds to C
y = 59

4. Divide each side by 27.25 to isolate the variable.
City officials want to know the height of a traffic light. Find the height of the traffic light (round to the nearest hundredths).
27.25 15
48.75 h =
Write a proportion.
h ft
27.25h =
Cross multiply.
227.25
227.25
Divide each side by to isolate the variable.
h ≈ 26.83
27.25 ft
48.75 ft
The traffic light is about 27 feet tall.

5. Triangles DEF and GHI are similar. Find the length of side HI.
Check It Out: Example 1
Triangles DEF and GHI are similar. Find the length of side HI. H G I
8 in x E D F
7 in
2 in
Triangles DEF and GHI are similar.

6. Understand the Problem
Additional Example 2: Problem Solving Application
A 30-ft building casts a shadow that is 75 ft long. A nearby tree casts a shadow that is 35 ft long. How tall is the tree? 1
Understand the Problem
The answer is the height of the tree.
List the important information:
• The length of the building’s shadow is 75 ft.
• The height of the building is 30 ft.
• The length of the tree’s shadow is 35 ft.

7. Additional Example 2 Continued
Make a Plan
Use the information to draw a diagram.
35 feet
75 feet
30 feet h

8. Additional Example 2 Continued
Solve 3 30 75 h 35
Corresponding sides of similar figures are proportional. =
75h = 1050
Find the cross products.
75h 75
1050 75 =
Divide both sides by 75.
h = 14
The height of the tree is 14 feet.