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Name: _____________________________ Geometry Ch. 4.5: Proving Triangles Congruent: ASA, and AAS In the last section, we learned that we could use Side-Side-Side and Side-Angle-Side to show that two triangles are congruent. We will now learn the last 2 which are Angle-Side-Angle and Angle-Angle-Side. Postulate 4.3: Angle-Side-Angle (ASA) Congruence If two angles and the _____________side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are ______________. Theorem 4.5: Angle-Angle-Side (AAS) Congruence If two angles and the __________________ side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are ________________. Concept Summary SSS SAS Proof of Theorem 4.5 Given: ∠L ≅ ∠Q , ∠M ≅ ∠R , MN ≅ RS Prove: △LMN ≅△QRS ASA AAS Name: _____________________________ Write a two-column proof Given: L is the midpoint of WE WR ! ED Prove: △WRL ≅△EDL Write a paragraph proof Given: ∠NKL ≅ ∠NJM KL ≅ JM Prove: LN ≅ MN Geometry Ch. 4.5: Proving Triangles Congruent: ASA, and AAS