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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.
 Example 1  
Given AB = XZ, AC = ZY, ACB = ZYX = 90°
Prove ABC XYZ
Hypotenuse Leg Theorem
 The following proof simply shows that it does not matter which of the two (corresponding) legs in the two right triangles are congruent.
 Example 2  
Given AB = XZ, CB = XY, ACB = ZYX = 90°
Prove ABC XYZ
Hypotenuse Leg Theorem Example