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Integrated Math 1 Extended - Unit 6 Name: __________________________ 6.2- Triangle Congruency Date: _____________ Period: ______ Objective: To determine which postulate (ASA, SSS, SAS, AAS) would be used to prove triangles are congruent. WARM UP: VOCABULARY: Included Side: The side that connects the pair of angles that are corresponding. Included Angle: The angle that is formed by two pairs of corresponding sides. THEOREM: Reflexive Property (of equality): The property that states that any side or angle is congruent to itself. POSTULATES: Side- Side- Side (SSS): To prove that two triangles are congruent by using all three corresponding sides. Side- Angle- Side (SAS): To prove that two triangles are congruent by using two pairs of corresponding sides and the pair of included angles. Angle- Side- Angle (ASA): To prove that two triangles are congruent by using two pairs of corresponding angles and the pair of included sides. Angle- Angle- Side (AAS): To prove that two triangles are congruent by using two pairs of corresponding angles and a pair of non-included sides. Example #1: Determine which postulate should be used to prove the triangles are congruent based on the information in the diagram. If there is no postulate to prove the triangles are congruent, write “NONE”. A.) B.) C.) D.) E.) F.) G.) H.) Example #2: Determine which postulate should be used to prove the triangles are congruent and write the triangle congruency statement. If there is no postulate to prove the triangles are congruent, write “NONE”. A.) ∆𝐴𝐶𝐵 ≅ ______________ by: B.) ∆𝐴𝐷𝐶 ≅ ______________ by: C.) ∆𝐴𝐵𝐶 ≅ ______________ by: E.) ∆ ____ __ ≅ ∆____ D.) ∆𝐷𝐸𝐶 ≅ ______________ by: G.) Given: I is the midpoint of ̅̅̅̅̅ 𝑀𝐸 and ̅̅̅ 𝑆𝐿 ∆ ____ __ ≅ ∆_________ I.) ∆ ____ __ ≅ ∆_________ by: F.) ∆ ____ __ ≅ ∆_________ by: H.) Given: ⃗⃗⃗⃗ 𝐼𝐻 bisects ∠𝑊𝐼𝑆 ∆ ____ __ ≅ ∆_________ by: by: by: J.) ∆ ____ __ ≅ ∆_________ by: Example #3: Determine what additional information is needed to prove the triangles are congruent based off the postulate and explain why. A.) SAS B.) AAS C.) SSS D.) ASA E.) SAS F.) ASA G.) SAS H.) SSS I.) SAS