Similarity and Ratios

Two figures are similar if they have the same shape.
-  Two or more figures are similar if the corresponding angles are equal, and the corresponding sides are in proportion.

Examples:


 

Example 1. 

The following triangles are similar. What is the value of the unknown side?

Example 2.   
Solution: Find the corresponding sides and write a proportion.
. Now, use the cross product to solve for :
.

Divide both sides by 8. Then:
The missing side is 12.

Example 3.  Two rectangles are similar. The first is 5 feet wide and 15 feet long. The second is 10 feet wide. What is the length of the second rectangle?
Solution: Let’s put for the length of the second rectangle. Since two rectangles are similar, their corresponding sides are in proportion. Write a proportion and solve for the missing number.

The length of the second rectangle is 30 feet.