Congruent Triangles - Hypotenuse Leg Theorem

Hypotenuse Leg Theorem

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

In the right triangles ΔABC and ΔPQR , if AB = PR, AC = QR then ΔABC ≡ ΔRPQ .

Example:

State whether the following pair of triangles are congruent. If so, state the triangle congruence and the postulate that is used.

Solution:

From the diagram, we can see that

• ΔABC and ΔPQR are right triangles

• AC = PQ (hypotenuse)
• AB = PR (leg)

The following video shows more examples of the Hypotenuse Leg (HL) Theorem and the Angle-Angle-Side (AAS) Theorem

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