Hypotenuse-Leg Theorem (HL) of Congruence

Definition: Any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

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Example: Determine if the triangles are congruent.

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Solution:

The given triangles are marked to show which parts are congruent. Using this information we can decide if the triangles are congruent.

Step 1: According to the given figure:
Hypotenuse AC is congruent to hypotenuse QR,
Leg BC is congruent to leg PR

Step 2: The Hypotenuse-Leg Theorem (HL) of congruence tells us if two right triangles have a congruent hypotenuse and a corresponding, congruent leg, then the triangles are congruent.

We can conclude that these triangles are congruent according to the HL Theorem, We can write this as:

∆ABC ≅ ∆QPR, which reads “Triangle ABC is congruent to Triangle QPR”.

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