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Transcript
Objectives • Prove that two triangles are similar using AA, SAS, and SSS 1 Proving Two Triangles Similar with Shortcuts • Instead of using the definition of similarity to prove that two triangles are congruent (all corresponding angles are congruent and all corresponding sides are proportional), you can use three shortcuts: – Angle-Angle (AA) – Side-Angle-Side (SAS) – Side-Side-Side (SSS) 2 Angle-Angle (AA) Similarity Postulate • If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. 3 AA Example Explain why the triangles are similar and write a similarity statement. ∠R ≅ ∠V (Given) ∠RSW ≅ ∠VSB (vertical angles are congruent) ΔRSW ≅ ΔVSB (AA) 4 Side-Angle-Side (SAS) Similarity Theorem • If an angle of one triangle is congruent to an angle of a second triangle and the sides including the two angles are proportional, then the triangles are similar. G A 2 4 B 3 C J ΔABC ~ ΔGJH 6 H 5 SAS Example Explain why the two triangles are similar and write a similarity statement. ∠Q ≅ ∠X since they are right angles The two sides that include the right angles are 3 6 proportional 4 8 By SAS, ΔPRQ ~ΔZYX 6 Side-Side-Side (SSS) Similarity Theorem • If the corresponding sides of two triangles are proportional, then the triangles are similar. G A 4 5 8 B 6 10 C J ΔABC ~ ΔGJH 12 H 7 SSS Example Explain why the two triangles are similar and write the similarity statement. AC CB AB 3 EG GF EF 4 Since all sides of the two triangles are proportional, by SSS, ΔABC ~ ΔEFG 8