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