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.

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.

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

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.