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4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Corresponding Parts of Congruent Triangles Side-Side-Side (SSS) If, in two triangles: three sides of one are congruent to three sides of the other, then the triangles are congruent. E B F C D A Side-Angle-Side (SAS) Angle-Side-Angle (ASA) If, in two triangles: If, in two triangles: two sides and the included angle of one are congruent to two sides and the included angle of the other, then the triangles are congruent two angles and the included side of one are congruent to two angles and the included side of the other, then the two triangles are E congruent. E B B F C D A F C D A Using only the given information, which pairs of triangles are congruent? Justify your answer. Angle-Angle-Side (AAS) If, in two triangles: two angles and a non-included side of one are congruent respectively to two angles and the corresponding non-included side of the other, then the triangles are congruent. 1. 2. E No Yes; SAS B 3. F C A D No 1 Ex. 1 Writing Proofs Given: N is the midpoint of UC F C N U C Prove: FUN 3 congruent Prove ___ parts of one triangle are ____________ to the _________________ parts of another corresponding triangle. ACN Statement 3 1). N is the midpoint of UC U C U A Reason 1). Given Use Triangle Congruence Theorems and other theorems in the proof. Ex. 2 L Given: mPLT 90, mLTO 90 and LP TO Prove: LTO TLP P Given: AE bisects BAD B D T Prove: ABC ADC O Reason Statement 1). mPLT 90, mLTO 90 Statement 1). AE bisects BAD B D 1). Given and LP TO Ex. 4 K J Given: KJ ML and KJ LM Prove: KJL LMK Statement 1). KJ ML and KJ LM M A Ex. 3 B C D E Reason 1). Given Corresponding Parts of Congruent Figures are Congruent (CPCFC) L Reason 1). Given If two figures are congruent, then so are all of their corresponding parts. 2 Ex. 5 W 2 Given: 1 3; 2 4 Prove: WA IT Statement 1). 1 3; 2 4 A 1 3 4 T I Reason 1). Given 3