HL Congruence

How to use the HL congruence to show that the given right triangles are congruent: postulate, 1 example, and its solution.

Postulate

Postulate

For two right triangles,
if a hypotenuse and a leg of each triangle
are congruent,
then those two right triangles are congruent.

This is the HL congruence postulate.
(Hypotenuse-Leg congruence)

Example

Example

Solution

To write a two-column proof,
make a two-column form like this.

To use the HL congruence postulate,
first show that
△ABC and △DCB are right triangles.

So start from the first given statement:
∠A and ∠D are right angles.

∠A and ∠D are right angles.

Then, by the definition of a right triangle,
△ABC and △DCB are right triangles.

Next, show that
the hypotenuses and the legs are congruent.

Use the other given statement:
ABCD.

BC is congruent to itself:
BCBC.

This is the reflexive property.

For two right triangles △ABC and △DCB,
the hypotenuse and a leg of each triangle
are congruent.

BCBC
ABCD

Then, by the HL congruence postulate,
△ABC and △DCB are congruent.

You found the Prove statement
△ABC ≅ △DCB.

So close the two-column form
by drawing the bottom line.

This is the proof of the example.