Congruence SSS and SAS 4 5 Triangle Warm

Congruence: SSS and SAS 4 -5 Triangle Warm Up Lesson Presentation Lesson Quiz Holt. Geometry Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Warm Up 1. Name the angle formed by AB and AC. Possible answer: A 2. Name three sides of ABC. AB, AC, BC 3. ∆QRS ∆LMN. Name all pairs of congruent corresponding parts. QR LM, RS MN, QS LN, Q L, R M, S N Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Objectives Apply SSS and SAS to construct triangles and solve problems. Prove triangles congruent by using SSS and SAS. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Vocabulary triangle rigidity included angle Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS In order to prove polygons are congruent, you must show that corresponding sides are congruent. Triangle rigidity gives a short cut to show triangles are congruent. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS COPY THIS SLIDE: 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 Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS COPY THIS SLIDE: Remember! Adjacent triangles share a side, so the side they share is a pair of congruent parts (this is called the reflexive property). Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Example 1: Using SSS to Prove Triangle Congruence COPY THIS SLIDE: Is ∆ABC ∆DBC? Explain. Yes, AC DC and AB DB because of the congruency marks. BC because of the reflexive property. So, ∆ABC ∆DBC by SSS. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Check It Out! Example 1 Is ∆ABC ∆CDA? Explain. Yes, AB CD and BC DA b/c of congruency marks. AC CA b/c of the reflexive property. So ∆ABC ∆CDA by SSS. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS COPY THIS SLIDE: 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 Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS 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. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS COPY THIS SLIDE: Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS COPY THIS SLIDE: Caution The letters SAS are written in that order because the angle must be between the sides. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Example 2: Engineering Application COPY THIS SLIDE: Is ∆XYZ ∆VWZ? Explain. Yes, XZ VZ and YZ WZ b/c of congruency marks. XZY VZW b/c they are vertical angles. Therefore ∆XYZ ∆VWZ by SAS. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Check It Out! Example 2 COPY THIS SLIDE: Is ∆ABC ∆DBC? Explain Yes, BA BD and ABC DBC b/c of congruency marks. BC b/c of the reflexive property. So ∆ABC ∆DBC by SAS. Holt Mc. Dougal Geometry

4 -5 Triangle Congruence: SSS and SAS Examples: Which postulate, if any, can be used to prove the triangles congruent? 2. Holt Mc. Dougal Geometry none 3. SSS

4 -5 Triangle Congruence: SSS and SAS Classwork/Homework • 4. 5 SSS, SAS, ASA, AAS W/S Holt Mc. Dougal Geometry