Ratios in similar polygons 7.2

Figures that are similar (~) have the same shape but not necessarily the same size.

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

Example 1: Describing Similar Polygons Identify the pairs of congruent angles and corresponding sides. 0.5

A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.

Example 2: Identifying Similar Polygons Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. rectangles ABCD and EFGH

Triangle Similarity 7.3

Example 1: Using the AA Similarity Postulate Explain why the triangles are similar and write a similarity statement. AB||DE

Example 2A: Verifying Triangle Similarity Verify that the triangles are similar. ∆PQR and ∆STU

Example 2B: Verifying Triangle Similarity Verify that the triangles are similar. ∆DEF and ∆HJK

Example 3: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD. Step 1 Prove triangles are similar.

Example 3 Continued Step 2 Find CD.

Your Turn! 1. Explain why the triangles are similar and write a similarity statement. 2. Explain why the triangles are similar, then find BE and CD.