# Using Similar Figures

## Lesson Preview

## What You'll Learn- To identify similar figures
- To find missing lengths in similar figures
## … And WhyTo measure distances indirectly, as in Example 3 |

## Identifying Similar Figures

### Investigation:Exploring Similar Figures

- Which pairs of figures have the same shape but not necessarily the same size?
- What is true about the angles of the figures with the same shape?

When two figures have the same shape, but not necessarily the same size, they are similar. In the similar triangles below, corresponding angles have the same measure. Since = = , the corresponding sides are proportional. You write Δ*ABC* ~ Δ*FGH*, where the symbol ~ means "is similar to."

A polygon is a closed plane figure formed by three or more line segments that do not cross.

### Similar Polygons

Two polygons are similar if

- corresponding angles have the same measure, and
- the lengths of corresponding sides form equal ratios.

#### Verifying That Figures Are Similar

Verify that the triangles are similar.

dThe measures of *X* and *P* are 76.5°. The measures of *Y* and *Q* are 41.5°. The measures of *Z* and *R* are 62°. = , = , and = .

The measures of corresponding angles are equal. The lengths of corresponding sides form equal ratios. So the triangles are similar.

Interactivity Similar polygons