1. 4.4 Proving Congruence – SSS and SAS What you’ll learn: 1.To use SSS Postulate to test for triangle congruence. 2.To use the SAS Postulate to test for triangle congruence.

2. More ways to prove 2 triangles are  : Postulate 4.1 SSS Congruence If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Postulate 4.2 SAS Congruence If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

3. Determine whether  ABC  DEF. Explain. A(-6,1), B(1,2), C(-1,-4), D(0,5), E(7,6), F(5,0)

4. Assumables The following can be assumed from the given picture: 1.Vertical angles are congruent. (reason: vert.  congruent) 2.A segment or angle shared by both triangles is congruent to itself. (reason: reflexive)

5. Given: RQ  TS, RQ  TS Prove:  QRT  STR 1.RQ  TS, RQ  TS 2.  QRT  RTS 3.RT  RT 4.  QRT  STR 1.Given 2.Alt. int. angles  3.Reflexive 4.SAS RS T Q

6. Determine which postulate can be used to prove that the triangles are congruent. Write “not possible” if no theorem applies. 1. Yes, SSS 2. Not possible 3. Yes, SAS

7. How to use CPCTC When you are asked to prove that corresponding parts (angles or sides) of 2 triangles are congruent, you may have to prove the 2 triangles are congruent first. Then by CPCTC, the corresponding parts are also congruent. Ex: Given:  B  D, AB  AD, BC  CD. Prove:  BAC  DAC StatementsReasons  B  D, AB  AD, BC  CD given  CBA  CDASAS  BAC  DACCPCTC A B C D

8. Homework p. 204 10-22 even