Aim: How to prove triangles are congruent using a 4 th shortcut: AAS.

1. Aim: How to prove triangles are congruent using a 4th shortcut: AAS. Do Now: • What method shows these triangles to be congruent? ASA SAS

2. Angle-Angle-Side IV.AAS = AAS A A’ B C B’ C’ If A = A', C = C', BC = B’C', then DABC = DA'B'C'. IfAAS  AAS, then the triangles are congruent Two triangles cannot be proved to be congruent by AAA  AAA or SSA  SSA

3. Model Problems Is the given information sufficient to prove congruent triangles? C D NO YES A B YES YES

4. Model Problem BD bisects B and A  C. Explain why ADB  CDB. ABD  CBD – angle bisector cuts angle into two congruent parts (A  A) A C – I’m told so - Given (A  A) BD  BD – anything is equal to itself - Reflexive Property (S  S) ADB  CDB because ofAAS  AAS

5. RM  PM RM  PM – Corresponding parts of congruent triangles are congruent CPCTC Model Problem - CPCTC RMP bisects AMB at M, and R  P. Explain why RM  PM AM  MB – bisector cuts segment into two congruent parts (S  S) R P – I’m told so - Given (A  A) RMA  PMB – Vertical angles are  (A  A) RMA  PMB because ofAAS  AAS

6. Model Problem