# HL Congruence

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

## 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

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:

AB ≅ CD.

BC is congruent to itself:

BC ≅ BC.

This is the reflexive property.

For two right triangles △ABC and △DCB,

the hypotenuse and a leg of each triangle

are congruent.

BC ≅ BC

AB ≅ CD

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.