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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 1 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 D A 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 2 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 D A Using only the given information, which pairs of triangles are congruent? Justify your answer. 1. 2. No Yes; SAS 3. No 3 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 A Reason 1). Given U C 4 Ex. 2 Given: mPLT 90, mLTO 90 and LP TO Prove: LTO TLP Statement 1). mPLT 90, mLTO 90 P L T O Reason 1). Given and LP TO A Ex. 3 Given: AE bisects BAD B D Prove: ABC ADC Statement 1). AE bisects BAD B D B C D E Reason 1). Given 5 Ex. 4 K Given: KJ ML and KJ LM Prove: KJL LMK Statement 1). KJ ML and KJ LM M J 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. 6 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 7