Proving Triangles Congruent—SSS, SAS SAS Postulate Another way to show that two triangles are congruent is to use the Side-Angle-Side (SAS) Postulate. If two sides and the included angle of one triangle are congruent to two sides and the included SAS Postulate angle of another triangle, then the triangles are congruent. Example: For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate. a. b. c. The right angles are congruent and The included angles, and In the is not △ABC, they are the included angles for the are congruent because they are by the sides and AB “included” So the triangles cannot be congruent sides. alternate interior angles for two AC. △DEF ≅ △JGH proved congruent by the SAS by the SAS Postulate. parallel lines. by △PSR ≅ △RQP Postulate. the SAS Postulate. Exercises Write the specified type of proof. Write a two column proof. Write a two-column proof. 1. 2. Given: = Given: = NP PM, AB CD, ∥ Prove: Prove: △NPL ≅ △MPL △ACD ≅ △CAB 3. Write a paragraph proof. Given: is the midpoint of V is the midpoint of V Prove: △XVZ ≅ △WVY
Proving Triangles Congruent—SSS, SAS SAS Postulate Another way to show that two triangles are congruent is to use the Side-Angle-Side (SAS) Postulate. SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. Example: For each diagram, determine which pairs of triangles can be proved congruent by the SAS Postulate. a. In △ABC, the is not “included” by the sides AB and AC. So the triangles cannot be proved congruent by the SAS Postulate. b. The right angles are congruent and they are the included angles for the congruent sides. △DEF ≅ △JGH by the SAS Postulate. c. The included angles, and are congruent because they are alternate interior angles for two parallel lines. △PSR ≅ △RQP by the SAS Postulate. Exercises Write the specified type of proof. 1. Write a two column proof. Given: NP = PM, Prove: △NPL ≅ △MPL 2. Write a two-column proof. Given: AB = CD, ∥ Prove: △ACD ≅ △CAB 3. Write a paragraph proof. Given: V is the midpoint of V is the midpoint of Prove: △XVZ ≅ △WVY
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