Chapter 4 Lesson 3 Objective: To prove two triangles congruent using the ASA Postulate and the AAS Theorem.

Postulate 4-3:  Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.     ∆HGB    ∆NKP

Example 1: Using ASA Name two triangles that are congruent by the ASA Postulate. because

Example 2: Proof of ASA Statements Reasons Given: CAB DAE, AB AE , ABC and AED are right angles. Prove: Statements Reasons 1.) 1.) Given CAB DAE, AB AE 2.) ABC and AED are right angles. 2.) Given 3.) ABC AED 3.) All rt. angles are congruent 4.) 4.) ASA

∆CDM ∆XGT Theorem 4-2: Angle-Angle-Side (AAS) Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.      ∆CDM   ∆XGT

Example 3: Proof of AAS Statements Reasons Given: S Q RP bisects SRQ. Prove: ∆SRP ∆QRP Statements Reasons 1.) RP bisects SRQ. 1.) Given 2.) Def. of angle bisector 3.) Given 4.) Ref. Prop. of congruent 5.) AAS

Example 4: Proof of AAS Given: || , bisects . Prove: ∆XMQ ∆RMT                                    Given:   || ,       bisects  . Prove: ∆XMQ  ∆RMT                                                                                                                                                                                                                                                              If || lines, alt. int. angles are congruent

Assignment pg. 197-200 #1-35