﻿ The Hypotenuse Leg Theorem for proving congruent triangles only works for right triangles, so the 1st thing you need to do is..

# Hypotenuse Leg Theorem

Proving Congruent Right Triangles

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

### Examples

##### Example 1

Given:AB = XZ, CB = XY, ACB = ZYX = 90°

Prove: ABC  XYZ

• ABC and XZY are right triangles since they both have a right angle
• AB = XZ (hypotenuse)  reason: given
• AC = ZY (leg) reason: given
• ABC  XYZ by the hypotenuse leg theorem which states that two right triangles are congruent if their hypotenuses are congruent and a corresponding leg is congruent. ##### Example 2

The following proof simply shows that it does not matter which of the two (corresponding) legs in the two right triangles are congruent

• ABC and XZY are right triangles since they both have a right angle
• AB = XZ (hypotenuse)  reason: given
• CB = XY (leg) reason: given
• ABC  XYZ by the hypotenuse leg theorem which states that two right triangles are congruent if their hypotenuses are congruent and a corresponding leg is congruent. ### Ultimate Math Solver (Free)

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