Warm-Up

• What is the scale factor (or similarity ratio) of the following two triangles?

6

9

15

8

12

20

Geometry 7-4

Properties of Similar Triangles

First Theorem

• If a line cuts through a triangle and is parallel to one side, the other two sides of the triangle are divided proportionally.

Example

• Find the length of US.

Example

• Find the length of NP.

Second Theorem

• An angle bisector divides its opposite side into two lengths that are proportional to the other sides of the triangle.

AB AC

DB DC

Example

• Find the length of PS and SR.

Example

• Find the length of SR and ST.