1. 3.8 HL Objectives: Use HL in proofs to prove triangles congruent.

2. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent. (HL) Hypotenuse-Leg Congruence Theorem (HL) A B C R S T 1.right triangle 2.hypotenuse 3.leg

3. 5 ways to prove triangles congruent: 1. SSS 2. SAS 3. ASA 4. AAS 5. HL (only rt. ∆’s)

4. Example 1: StatementsReasons 1. 2. 3. 4. 5. 6. 7. 8. Given Definition of perpendicular  DCE and  ACB are right angles Definition of midpoint Definition of congruent segments B A C D E DC = CB Given HL ∆ABC  ∆EDC ∆DCE and ∆ACB are right triangles Definition of right triangle

5. Example 2: StatementsReasons 1. 2. 3. 4. 5. 6. 7. All right angles are congruent Vertical Angles Theorem Given Definition of altitude  BGF,  ECF,  BGA,  ECD are right angles Definition of midpoint Definition of congruent segments  BGF   ECF BF = EF B E C D AGF Continued on next slide  BFG   EFC Given

6. Example 2: StatementsReasons 8. 9. 10. 11. 12. HL CPCTC Given B E C D AGF ∆BAG  ∆EDF AAS ∆BGF  ∆ECF Definition of right triangle ∆BAG and ∆EDF are right triangles