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Unformatted text preview: 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. ii. Given: Prove: A D, B E , AC DF ABC DEF c. If we can prove AB = DE then the two triangles will be congruent i. Three possibilities b/c of Trichotomy 1.
ii. 1) AB = CD 2) AB DE 3) AB DE d. If we can prove 2 and 3 are impossible then 1 holds. Suppose 2 holds AB F DE 1) A D, B E , AC DF 1) Given 2)Let Z be a point to where AZ = DE 3) DEF AZC 4) AZC DEF 5) AZC ABC But this impossible, why? 2)point plotting thm. 3) 4) 5) e. Suppose number 3 holds AB i. The proof is the same DE f. If 2 and 3 are impossible then 1 is must hold. ABC DEF by SAS, so SAA is valid i. Is SSA a Postulate? B) a. Theorem 7-4 (The Hypotenuse-Leg Theorem)
i. Given a correspondence between two right triangles. If the hypotenuse and one leg of one of the triangles are congruent to the corresponding parts of the second triangle, then the correspondence is a congruence ii. Example) If the diagonals of rectangle ABCD are congruent, prove that AB = CD 1) Quad. ABCD is a rectangle, BD = AC 2) BAD, CDA are right angles 3) ACD, DBA are right triangles 4) 5) 6) 1) Given 2) Def. of a rectangle 3) 4) 5) 6) ...
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This note was uploaded on 05/16/2011 for the course ALGEBRA 098 taught by Professor Johnson during the Spring '09 term at Grand Valley State University.
- Spring '09