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Transcript
Aim: How do we prove triangles congruent using the Angle-Angle-Side Theorem? Do Now: In each case, which postulate can be used to prove the triangles congruent? 1) 2) 3) S.A.S. S.S.S. 4) A.S.A. A.A.S. Theorem Theorem #20: Angle-Angle-Side Theorem (A.A.S.) If two angles and the non-included side are congruent to two angles and the corresponding non-included side of another triangle, the two triangles are congruent. 1 Ex: A.A.S Theorem In each case, state whether A.A.S. be used to prove the triangles congruent. 2) 1) 3) X Geometry Lesson: Angle-Angle-Side Theorem 2 Ex: A.A.S. Theorem Given: RG MT M T Prove: MG TG R M G Statement Reason 1) RG MT 2) MGR, TGR are rt. 's 3) MGR TGR 4) M T 5) RG RG 6) MGR TGR 7) MG TG T 1) Given 2) Def. perpendicular lines 3) Right 's are congruent. 4) Given 5) Reflexive Postulate 6) A.A.S. Theorem 7) C.P.C.T.C. Geometry Lesson: Angle-Angle-Side Theorem 3 P Ex: 1,2,3 A.A.S. Theorem: R 1) Given: BP bisects RPM R M Prove: PRB PMB M B 2) Given: Isosceles DES with SD SE ET DS , DR ES Prove: ET DR S T D 3) Given: MPV bisects HPK H K Prove: MP VP R E H P V M Geometry Lesson: Angle-Angle-Side Theorem K 4 Ex: 4, 5 A.A.S. Theorem: 4) In ABC and EFG, mA 42, mB 68, CA 12 cm, mF 42, mG 68, and EF 12 cm. Is ABC FGE? Explain. 5) In ABC and EFG, mA 50, AB 20, BC 16, mE 50, EF 20, and FG 12. Is ABC EFG? Explain. Geometry Lesson: Angle-Angle-Side Theorem 5