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

4-5 Triangle Congruence: SSS and SAS Warm Up 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. Possible answer: A QR  LM, RS  MN, QS  LN, Q  L, R  M, S  N AB, AC, BC

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

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

Holt McDougal 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 McDougal Geometry 4-5 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. COPY THIS SLIDE:

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

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

Holt McDougal 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 McDougal Geometry 4-5 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. COPY THIS SLIDE:

Holt McDougal 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 McDougal Geometry 4-5 Triangle Congruence: SSS and SAS COPY THIS SLIDE:

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

Holt McDougal Geometry 4-5 Triangle Congruence: SSS and SAS Example 2: Engineering Application 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. COPY THIS SLIDE:

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

Holt McDougal Geometry 4-5 Triangle Congruence: SSS and SAS Examples: Which postulate, if any, can be used to prove the triangles congruent? noneSSS

Holt McDougal Geometry 4-5 Triangle Congruence: SSS and SAS Classwork/Homework 4.5 SSS, SAS, ASA, AAS W/S