4 4 Triangle Congruence SSS and SAS Geometry

4 -4 Triangle Congruence: SSS and SAS Geometry A Bellwork 3) Write a congruence statement that indicates that the two triangles are congruent. A D B C Holt Geometry

Congruence: SSS and SAS 4 -4 Triangle Holt Geometry

4 -4 Triangle Congruence: SSS and SAS In Lesson 4 -1, you proved triangles congruent by showing that all six pairs of corresponding parts were congruent. Now we will learn of several shortcuts to prove triangles congruent. We can prove them congruent using SIDE-SIDE or SIDE-ANGLE-SIDE. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS 4 -1 Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Remember! Adjacent triangles 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 Example 1: Using SSS to Prove Triangle Congruence Use SSS to explain why ∆ABC ∆DBC. It is given that AC DC and that AB DB. By the Reflexive Property of Congruence, BC BC. Therefore ∆ABC ∆DBC by SSS. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Check It Out! Example 1 Use SSS to explain why ∆ABC ∆CDA. It is given that AB CD and BC DA. By the Reflexive Property of Congruence, AC CA. So ∆ABC ∆CDA by SSS. 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 4 -2 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 Check It Out! Example 2 Use SAS to explain why ∆ABC ∆DBC. It is given that BA BD and ABC DBC. By the Reflexive Property of , BC BC. So ∆ABC ∆DBC by SAS. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Example 3 A: Verifying Triangle Congruence Determine if we know these triangles are congruent by SSS or SAS. ∆MNO ∆PQR. PQ MN, QR NO, PR MO ∆MNO ∆PQR by SSS. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Example 3 B: Verifying Triangle Congruence Determine if we know these triangles are congruent by SSS or SAS. ∆STU ∆VWX. ST VW, TU WX, and T W. ∆STU ∆VWX by SAS. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Check It Out! Example 3 Determine if we know these triangles are congruent by SSS or SAS. ∆ADB ∆CDB by SAS. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Example 4: Proving Triangles Congruent Determine if we know these triangles are congruent by SSS or SAS. ∆ABD ∆CDB by SAS. Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Lesson Quiz: Part I Can SSS or SAS or none be used to prove the triangles congruent? 1. none 2. SSS Holt Geometry

4 -4 Triangle Congruence: SSS and SAS Example 2: Engineering Application The diagram shows part of the support structure for a tower. Use SAS to explain why ∆XYZ ∆VWZ. It is given that XZ VZ and that YZ WZ. By the Vertical s Theorem. XZY VZW. Therefore ∆XYZ ∆VWZ by SAS. Holt Geometry