This document discusses two postulates for proving triangles congruent: the Side-Side-Side (SSS) postulate and the Side-Angle-Side (SAS) postulate. It provides examples of proofs using each postulate, demonstrating how to prove triangles congruent by showing that three sides or two sides and the included angle are congruent between the two triangles. The document includes practice problems applying these postulate proofs.

1. Geometry - 4.4 Proving Triangles Congruent using SSS and SAS

2. Side-Side-Side Congruence Postulate SSS Post. - If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If then,

3. Using SSS Congruence Post. 1) 2) 1) Given 2) SSS Prove:

4. Side-Angle-Side Congruence Postulate SAS Post. – If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If then,

6. Using SAS Congruence Post. 1) 2) 3) 1) Given 2) Vertical Angles 3) SAS Prove:

7. Proof 1) MB is perpendicular bisector of AP 2) <ABM and <PBM are right <‘s 3) 4) 5) 6) 1) Given 2) Def of Perpendiculars 3) Def of Bisector 4) Def of Right <‘s 5) Reflexive Property 6) SAS Given: MB is perpendicular bisector of AP Prove:

8. Proof 1) O is the midpoint of MQ and NP 2) 3) 4) 1) Given 2) Def of midpoint 3) Vertical Angles 4) SAS Given: O is the midpoint of MQ and NP Prove:

9. Proof 1) 2) 3) 1) Given 2) Reflexive Property 3) SSS Given: Prove:

10. Proof 1) 2) 3) 4) 1) Given 2) Alt. Int. <‘s Thm 3) Reflexive Property 4) SAS Given: Prove:

11. Practice Problems Pg. 266 #4, 12, 13, 15, 21, 25 #4 and 15 (prove triangles congruent only) HW Check Next Class