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4.5 – Prove Triangles Congruent by ASA and AAS Geometry Ms. Rinaldi Angle-Side-Angle (ASA) Congruence Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. If Angle A R Side CA TR Angle C T Then ABC RST B C A S T R EXAMPLE 1 Use ASA Decide whether the congruence statement is true. Explain your reasoning. ABC JKL SOLUTION (A) B K (S) BA KJ (A) A J So, by ASA, ABC JKL EXAMPLE 2 Use ASA Decide whether the congruence statement is true. Explain your reasoning. LMN PON Angle-Angle-Side (AAS) Congruence Postulate If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of a second triangle, then the two triangles are congruent. If Angle A R Angle C T Side BC ST Then ABC RST B C A S T R EXAMPLE 3 Use AAS Decide whether the congruence statement is true. Explain your reasoning. RST TUR SOLUTION U S (A) URT STR (A) (S) RT RT So, by AAS, RST TUR EXAMPLE 4 Use AAS Decide whether the congruence statement is true. Explain your reasoning. HDE FGE EXAMPLE 5 Use ASA or AAS State the third congruence that must be given to prove that ABC DEF using the indicated postulate. B Given: A D E AB DE Use the ASA Congruence Postulate. C A D F EXAMPLE 6 Use ASA or AAS State the third congruence that must be given to prove that ABC DEF using the indicated postulate. B Given: C F E B E Use the ASA Congruence Postulate. C A D F EXAMPLE 7 Use ASA or AAS State the third congruence that must be given to prove that ABC DEF using the indicated postulate. B Given: A D E C F Use the AAS Congruence Postulate. C A D F