What Is the Hypotenuse Angle Theorem?

The Hypotenuse Angle Theorem states that if one of the acute angles and the hypotenuse of a right triangle are congruent to the corresponding acute angle and hypotenuse of a second triangle, \this proves that the two triangles are also congruent. In math, this theorem is one of a few theorems used to prove right triangle congruency.

This theorem is valid for right triangles, or triangles in which there is a 90-degree angle. In a right triangle, the hypotenuse is the longest side or leg of the triangle. The hypotenuse also is opposite the 90-degree angle.

Likewise, the Pythagorean Theorem relates the three sides of a right triangle. In a right triangle where side “c” is the hypotenuse length and “b” and “an” are the two other side lengths, this theorem states that the hypotenuse length squared is equal to the sum of the each side length squared.

Besides using an acute angle and the hypotenuse of a right triangle to prove congruency, one can also use the leg and hypotenuse of two right triangles. This theorem is called the Hypotenuse Leg Theorem and states that if there are two right triangles that have a congruent hypotenuse and a corresponding congruent leg, then the two right triangles are also congruent.