1. Congruence in Right Triangles
Academic Geometry

2. The HL Theorem
In a right triangle, the side opposite the right angle is the longest side and is called the hypotenuse. The other two sides are called legs.
hypotenuse
leg
leg

3. The HL Theorem
Right triangles provide a special case for congruence. There is an SSA congruence rule. It occurs when the hypotenuses are congruent and one pair of legs are congruent.

4. Theorem 4-6
Hypotenuse-Leg (HL) Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

5. The HL Theorem Which two triangles are congruent by the HL Theorem? p5 3 5 3 l r s 5 3 o q n m t

6. The HL Theorem
Are these triangles congruent using the HL Theorem?

7. HL Theorem To use the HL Theorem 3 conditions must be met:
There are 2 right triangles
The triangles have congruent hypotenuses
There is one pair of congruent legs

8. Using the HL Theorem
Given: CD congruent EA, AD is the perpendicular bisector of CE
Prove: Triangle CBD congruent Triangle EBA
Statements Reasons c a b d e

9. Using the HL Theorem
Given: WJ congruent KZ and <W and <K are right angles. Prove: Triangle JWZ congruent Triangle ZKJ Statements Reasons w z j k

10. Using the HL Theorem
Given <PRS and <RPQ are right angles. SP congruent QR. Prove: Triangle PRS congruent Triangle RPQ Statements Reasons p q s r