HL Congruence (Hypotenuse-Leg Congruence)

HL Congruence (Hypotenuse-Leg Congruence)

How to solve HL congruence problems: postulate, example and its solution (proof).

Postulate

HL Congruence: If the hypotenuse and the leg of a right triangle are congruent to the hypotenuse and the leg of another right triangle, then those two right triangles are congruent.

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

Example

Given: angle A and angle D are right angles, line segment AB is congruent to line segment CD. Prove: triangle ABC is congruent to triangle DCB.

First, show that △ABC and △DCB are right triangles.

A and ∠D are right angles.

So △ABC and △DCB are right triangles.

BC is equal to itself.
So BCBC.

Use the given statement.
ABCD

The hypotenuse and the leg of △ABC
are congruent to
the hypotenuse and the leg of △DCB.

Then, by the HL congruence postulate,
ABC ≅ △DCB.