7 3 Triangle Similarity AA SSS SAS Objectives

7 -3 Triangle Similarity: AA, SSS, SAS Objectives Prove certain triangles are similar by using AA, SSS, and SAS. Use triangle similarity to solve problems. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 1 Explain why the triangles are similar and write a similarity statement. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 2 A: Verifying Triangle Similarity Verify that the triangles are similar. ∆PQR and ∆STU Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 2 B Verify that ∆TXU ~ ∆VXW. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 3 A: Finding Lengths in Similar Triangles Explain why ∆ABE ~ ∆ACD, and then find CD. Step 1 Prove triangles are similar. Step 2 Find CD. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 3 B Explain why ∆RSV ~ ∆RTU and then find RT. Step 1 Prove triangles are similar. Step 2 Find RT. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 4 A: Writing Proofs with Similar Triangles Given: 3 UT = 5 RT and 3 VT = 5 ST Prove: ∆UVT ~ ∆RST 1. Statements 1. 2. 3. 4. 5. 6. Holt Mc. Dougal Geometry Reasons

7 -3 Triangle Similarity: AA, SSS, SAS Example 4 B Given: M is the midpoint of JK. N is the midpoint of KL, and P is the midpoint of JL. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 4 B Continued Statements Reasons 1. 2. 3. 4. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 5: Engineering Application The photo shows a gable roof. AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot. From p. 473, BF 4. 6 ft. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS You learned in Chapter 2 that the Reflexive, Symmetric, and Transitive Properties of Equality have corresponding properties of congruence. These properties also hold true for similarity of triangles. Holt Mc. Dougal Geometry