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7.4 - Copy - 7-4 Congruence Theorems Based on the Exterior...

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7-4 Congruence Theorems Based on the Exterior Angle Theorem A) Theorem 7-3 (The SAA (AAS) Theorem) a. Every SAA correspondence is a congruence b. Proof: i. Given: DF AC E B D A 2245 2245 2245 , , ii. Prove: DEF ABC 2245 c. If we can prove AB = DE then the two triangles will be congruent i. Three possibilities b/c of Trichotomy 1. DE AB DE AB CD AB ° ) 3 ) 2 ) 1 = ii. If we can prove 2 and 3 are impossible then 1 holds. d. Suppose 2 holds DE AB F 1) DF AC E B D A 2245 2245 2245 , , 1) Given
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2)Let Z be a point to where AZ = DE 2)point plotting thm. 3) AZC DEF 2245 3) 4) DEF AZC 2245 4) 5) ABC AZC 2245 5) But this impossible, why? e. Suppose number 3 holds DE AB i. The proof is the same f. If 2 and 3 are impossible then 1 is must hold.
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