1. Learning Goals – Lesson 7:3
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.
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.
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.

2. Example 1B: Verifying Triangle Similarity
Verify that the triangles are similar.
A. ∆PQR and ∆STU
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.

3. Example 3A: Writing Proofs with Similar Triangles
There following properties we learned about congruence are also true for similarity of triangles.
Example 3A: Writing Proofs with Similar Triangles
Given: 3UT = 5RT and 3VT = 5ST
Prove: ∆UVT ~ ∆RST
Statements
Reasons

4. Example 2B: Engineering Application
Example 3B: Writing Proofs with Similar Triangles
Statements
Reasons
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.