7-3 Triangle Similarity: AA, SSS, and SAS

7.3.1: Explain how AA, SSS, and SAS can be used to show that triangles are

similar.

7.3.2: Use triangle similarity to solve problems.

7.3.3: Prove certain triangles are similar by using AA, SSS, and SAS.

Learning Goals – Lesson 7:3

Example 1A: Using the AA Similarity Postulate

A. Explain why the triangles are similar and write a similarity statement.

B. Explain why the triangles are similar and write a similarity statement.

There are several ways to prove certain triangles are _____________. The following postulates will be used in proofs just as ______, ______, ______, ______, and ______ were used to prove triangles congruent.

7-3 Triangle Similarity: AA, SSS, and SAS

B. ∆DEF and ∆HJK

C. ∆TXU ~ ∆VXW.

Example 2A: Finding Lengths in Similar Triangles

Explain why ∆ABE ~ ∆ACD, and then find CD.

Step 1 Verify the triangles are similar.

Step 2 Find CD.

Example 1B: Verifying Triangle Similarity

Verify that the triangles are similar.

A. ∆PQR and ∆STU

7-3 Triangle Similarity: AA, SSS, and SAS

Example 3A: Writing Proofs with Similar Triangles

Given: 3UT = 5RT and 3VT = 5ST

Prove: ∆UVT ~ ∆RST

Statements Reasons

There following properties we learned about congruence are also true for similarity of triangles.

7-3 Triangle Similarity: AA, SSS, and SAS

Example 2B: Engineering Application

The photo shows a gable roof. Segments AC || FG. ∆ABC ~ ∆FBG. Find the measure of segment BA to the nearest tenth of a foot.

Statements Reasons

Example 3B: Writing Proofs with Similar Triangles