7 3 Triangle Similarity AA SSS and SAS

7 -3 Triangle Similarity: AA, SSS, and SAS 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 1 A: 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.

7 -3 Triangle Similarity: AA, SSS, and SAS Example 1 B: Verifying Triangle Similarity Verify that the triangles are similar. A. ∆PQR and ∆STU B. ∆DEF and ∆HJK C. ∆TXU ~ ∆VXW. Example 2 A: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD. Step 1 Verify the triangles are similar. Step 2 Find CD.

7 -3 Triangle Similarity: AA, SSS, and SAS There following properties we learned about congruence are also true for similarity of triangles. Example 3 A: Writing Proofs with Similar Triangles Given: 3 UT = 5 RT and 3 VT = 5 ST Prove: ∆UVT ~ ∆RST Statements Reasons

7 -3 Triangle Similarity: AA, SSS, and SAS Example 3 B: Writing Proofs with Similar Triangles Statements Reasons Example 2 B: 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.