Section 4.5 Notes: Proving Triangles Congruent – ASA, AAS

1. Section 4.5 Notes: Proving Triangles Congruent – ASA, AAS EQ: What information is sufficient to determine whether two triangles are congruent?

2. Included Side Two sides that form an angle. B Side from the included angle ∠BAC A C

3. CPCTC Corresponding Parts of Congruent Triangles are Congruent D A We have proven that ∆DVA ≅ ∆EVN by SAS so therefore by CPCTC we can say that V N E

4. Angle-Side-Angle (ASA) Congruence If Angle ∠A ≅ ∠D Side Angle ∠C ≅ ∠F Then ∆ABC ≅ ∆DEF B A C E F D

5. Example 1: Label diagram! L is the midpoint of Midpoint Theorem ∠LED ≅ ∠LWR ∠WLR ≅ ∠ELD ∆WRL ≅ ∆EDL ASA

6. Try the you try first before looking at the answer!!!

7. You Try! Alternate Interior Angles ∠ABD ≅ ∠EBC ASA ∆ABD ≅ ∆EBC

8. Angle-Angle-Side Congruence If Angle ∠A ≅ ∠D Angle ∠B ≅ ∠F Side Then ∆ABC ≅ ∆DEF B A C E F D

9. Example 2: ∠NKL ≅ ∠NJM Reflexive Property ∆NKL ≅ ∆NJM AAS CPCTC

10. Try the you try first before looking at the answer!!!

11. You Try! ∠F & ∠K are right angles Alternate interior angles ∠FHG ≅ ∠KGH ∠HFG ≅∠GKH ∆HFG ≅ ∆GKH AAS