![]() It is given that XZ VZ and that YZ WZ. It can also be shown that only two pairs of congruent corresponding sides are needed to prove the congruence of two triangles if the included angles are also congruent.Ĭaution The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides. B is the included angle between sides AB and BC. Check It Out! Example 1 Use SSS to explain why ∆ABC ∆CDA.Īn included angle is an angle formed by two adjacent sides of a polygon. By the Reflexive Property of Congruence, AC CA. Example 1: Using SSS to Prove Triangle Congruence Use SSS to explain why ∆ABC ∆DBC. By the Reflexive Property of Congruence, BC BC. It is given that AC DC and that AB DB. Remember! Adjacent triangles share a side, so you can apply the Reflexive Property to get a pair of congruent parts. This can be expressed as the following postulate. It states that if the side lengths of a triangle are given, the triangle can have only one shape.įor example, you only need to know that two triangles have three pairs of congruent corresponding sides. The property of triangle rigidity gives you a shortcut for proving two triangles congruent. In Lesson 4-3, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent. Vocabulary triangle rigidity included angle Prove triangles congruent by using SSS and SAS. Standard MCC9-12.G.SRT.5 Objectives Apply SSS and SAS to construct triangles and solve problems. Name all pairs of congruent corresponding parts. 1.Name the angle formed by joining AB and AC. ![]() Triangle Congruence: SSS and SAS Holt Geometry Warm Up Lesson Presentation Lesson Quiz Holt McDougal GeometryĪB, AC, BC QR LM, RS MN, QS LN, Q L, R M, S N
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