Name: ________________________________
Proportions in Similar Figures
Using proportions to find missing lengths in similar figures
A polygon is a closed plane figure formed by three or more line segments.
Two polygons are similar if:
1. corresponding angles have the same measure
2. the lengths of corresponding sides form equivalent ratios
Finding a Missing Measure
Triangles ABC and DEF are similar. Find the value of c
Write a proportion
𝑨𝑩
𝑨𝑪
𝒄
=
𝑫𝑬 𝑫𝑭
𝒄
𝟏𝟖
𝒄
Write the cross product
Divide each side by 3
Solve for c
𝟏𝟖
𝟑𝒄
𝟑
𝟔
=
𝟏𝟖 𝟗
=
=
𝟑𝟔
𝟑
C = 12
𝟐
𝟑
=
(simplify ratio if you can)
𝟐
𝟑
3c = 36
Multiple Choice
A 5-ft person standing near a tree has a shadow 12 ft long. At the
same time, the tree has a shadow 42 ft long. What is the height of the
tree?
A. 17.5 ft
B. 35 ft
C. 49 ft
D. 100.8 ft
Draw a picture and
let x represent the
height of the tree.
Write a proportion
𝒙
𝟒𝟐
=
𝟓 𝟏𝟐
𝒙
𝟓
=
𝟕
𝟐
𝒙
Write the cross product
Divide each side by 2
Solve for x
(simplify ratio if you can)
𝟓
𝟐𝒙
𝟐
=
=
𝟕
𝟐
2x = 35
𝟑𝟓
𝟐
x = 17.5
The height of the tree is 17.5 ft.
Important: Similar figures have the same shape, but not
necessarily the same size.