7 3 Triangle Similarity AA SSS SAS 7

7 -3 Triangle. Similarity: AA, SSS, SAS 7 -3 Triangle Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Warm Up Solve each proportion. 1. 2. 3. z = ± 10 x=8 4. If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides. Q X; R Y; S Z; Holt Mc. Dougal Geometry

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 COPY THIS SLIDE: There are several ways to prove certain triangles are similar. The following postulate, as well as the SSS and SAS Similarity Theorems, will be used in proofs just as SSS, SAS, ASA, HL, and AAS were used to prove triangles congruent. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Example 1: Using the AA Similarity Postulate COPY THIS SLIDE: Explain why the triangles are similar and write a similarity statement. BCA ECD because they are vertical angles. Also, A D because they are right angles. Therefore ∆ABC ~ ∆DEC by AA~. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Check It Out! Example 1 COPY THIS SLIDE: Explain why the triangles are similar and write a similarity statement. By the Triangle Sum Theorem, (180 -90 -43) m C = 47 o, so C F. B E because they are right angles. Therefore, ∆ABC ~ ∆DEF by AA ~. Holt Mc. Dougal Geometry

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

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

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

7 -3 Triangle Similarity: AA, SSS, SAS Example 2 B: Verifying Triangle Similarity COPY THIS SLIDE: Verify that the triangles are similar. ∆DEF and ∆HJK D H by the Definition of Congruent Angles. Therefore ∆DEF ~ ∆HJK by SAS ~. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Check It Out! Example 2 COPY THIS SLIDE: Verify that ∆TXU ~ ∆VXW. TXU VXW by the Vertical Angles Theorem. Therefore ∆TXU ~ ∆VXW by SAS ~. Holt Mc. Dougal Geometry

7 -3 Triangle Similarity: AA, SSS, SAS Classwork/Homework • 7. 3 #’s: 1 -6, 11 -16 Holt Mc. Dougal Geometry