3.8 HL

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

2. S B R T A C Hypotenuse-Leg Congruence Theorem (HL) 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) • right triangle • hypotenuse • leg

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

4. A Example 1: C D B E Given DCEand ACB are right angles Definition of perpendicular ∆DCEand∆ACBare right triangles Definition of right triangle Given DC = CB Definition of midpoint Definition of congruent segments Given ∆ABC ∆EDC HL

5. B Example 2: D C A G F E Given BGF, ECF, BGA,ECDare right angles Definition of altitude All right angles are congruent BGF ECF Vertical Angles Theorem BFGEFC Given Definition of midpoint BF = EF Definition of congruent segments Continued on next slide

6. B Example 2: D C A G F E ∆BGF ∆ECF AAS CPCTC Given ∆BAGand∆EDF are right triangles Definition of right triangle ∆BAG ∆EDF HL