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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

Related Topics: More Geometry Lessons

*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 Δ*ABC* and Δ*PQR* , if *AB* = *PR*, *AC = QR *then Δ*ABC* ≡ Δ*RPQ* .

*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

- Δ
*ABC*and Δ*PQR*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

HL Postulate (Lesson)

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

Practice problems and proofs using the HL (Hypotenuse-Leg) Postulate

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