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4-4 Triangle Congruence: SSS and SAS Bell Ringer 1. Name the angle formed by AB and AC. 2. Name the three sides of ABC. 3. ∆QRS ∆LMN. Name all pairs of congruent corresponding parts. Holt Geometry 4-4 Triangle Congruence: SSS and SAS In Lesson 4-3, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent. (3 pair of congruent sides and 3 pair of congruent angles) Luckily, there are shortcuts to prove that 2 triangles are congruent to each other. We will learn these today. Holt Geometry 4-4 Triangle Congruence: SSS and SAS For example, you only need to know that two triangles have three pairs of congruent corresponding sides. This can be expressed as the following postulate. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Remember! Some triangles can share a side, so you can apply the Reflexive Property to get a pair of congruent parts. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Explain why ∆ABC ∆DBC. Holt Geometry 4-4 Triangle Congruence: SSS and SAS An included angle is an angle formed by two adjacent sides of a polygon. B is the included angle between sides AB and BC. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Another shortcut uses two pairs of congruent sides and one pair of congruent INCLUDED angles. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Caution The letters SAS are written in that order because the congruent angles must be between pairs of congruent corresponding sides. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Example 2: Engineering Application The diagram shows part of the support structure for a tower. Explain why ∆XYZ ∆VWZ. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Explain why ∆ABC ∆DBC. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Example 4: Proving Triangles Congruent Given: BC ║ AD, BC AD Prove: ∆ABD ∆CDB Statements Holt Geometry Reasons 4-4 Triangle Congruence: SSS and SAS Check It Out! Example 4 Given: QP bisects RQS. QR QS Prove: ∆RQP ∆SQP Statements Holt Geometry Reasons 4-4 Triangle Congruence: SSS and SAS An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Holt Geometry 4-4 Triangle Congruence: SSS and SAS Example 2: Applying ASA Congruence Determine if you can use ASA to prove the triangles congruent. Explain. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Holt Geometry 4-4 Triangle Congruence: SSS and SAS Use AAS to prove the triangles congruent. Given: JL bisects KLM, K M Prove: JKL JML Holt Geometry 4-4 Triangle Congruence: SSS and SAS Holt Geometry 4-4 Triangle Congruence: SSS and SAS Example 4A: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know. Holt Geometry 4-4 Triangle Congruence: SSS and SAS Identify the postulate or theorem that proves the triangles congruent. Holt Geometry