Congruent Triangles - Hypotenuse Leg Theorem

In this lesson, we will learn

• the Hypotenuse-Leg Theorem
• why the Hypotenuse-Leg Theorem is enough to prove triangles congruent
• the proof of the Hypotenuse-Leg Theorem using a two-column proof
• how to prove triangle congruence using the Hypotenuse-Leg Theorem

Hypotenuse Leg Theorem

Hypotenuse Leg Theorem is used to prove whether a given set of right triangles are congruent. 

The Hypotenuse Leg (HL) Theorem states that

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 following 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)

Hypotenuse - Leg Congruence Theorem

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

Prove Triangle Congruence with HL Postulate

HL Postulate (Lesson)
A lesson and proof of the HL (Hypotenuse-Leg) postulate using a two-column proof

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