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

2. 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

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

4. 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

5. ∆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

6. 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

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

8. Assignment pg
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