4.5 Proving Congruence – ASA and AAS What you’ll learn: To use the ASA Postulate to test for triangle congruence. To use the AAS Theorem to test for triangle congruence.
2 more ways to prove 2 triangles Postulate 4.3 Angle-Side-Angle Congruence If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent. Theorem 4.5 Angle-Angle-Side Theorem If 2 angles and a nonincluded side of one triangle are congruent to the corresponding 2 angles and side of a 2nd triangle, then the 2 triangles are congruent.
Given: L is the midpoint of WE. WREDProve: WRLEDL R E L W 1. L is the midpoint of WE. WRED • WLLE • WE, RD • WRLEDL • Given • Midpoint theorem • Alt. int. s • AAS D
Given: NKLNJM, KLJMProve: LNMN J K L M N • NKLNJM, KLJM • NN • JMNKLN • LNMN • Given • Reflexive • AAS • CPCTC