Example 1
Given AB = XZ, AC = ZY, 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.
Example 2
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
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.