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