Congruence in Right Triangles

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? p l r s 5 5 5 o q 3 3 3 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