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

Theorems and Postulates for proving triangles congruent
 Hypotenuse Leg Theorem
 Side Side Side
 Side Angle Side
 Angle Side Angle
 Angle Angle Side
 isosceles triangle proofs
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 indirect proof
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 Worksheets & Activities on Triangle Proofs
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.