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Proving Triangles are Congruent: ASA and AAS Sec 4.4 GOAL: To prove triangles are congruent by using the ASA Congruence Postulate and the AAS Congruence Theorem 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. Included side – a side that is between two angles of a triangle B Q P A C If A P and AB PQ and B Q, then ABC PQR R AAS Congruence Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the two triangles are congruent. Nonincluded side – a side that is not between two consecutive angles of a triangle. Here, AC and PR are called nonincluded sides. B Q P A C If B Q and C R, and AC PR, then ABC PQR R Examples Is ABC DEC ? B A C D E Examples Is PQR SRQ ? Q P R S Examples Is PQR SRQ ? P R Q S Two – Column Proof Given: WZ bi sec ts XZY and XWY Prove: WZX WZY X W Z Y Example Decide whether enough information is given to prove that triangles are congruent. If yes, state the congruence postulate you would use and the congruence statement. P Q R S Example Solve for x and y (3 y 11) 55 (2 x)