Last month, we have discussed the proof of the Hypotenuse Leg Theorem. It states that if the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and leg of another triangle, then the two triangles are congruent. In this post, we are going to discuss a related theorem on right triangles, the Hypotenuse Angle Theorem or HA Theorem. The HA Theorem states that if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another triangle, then the two triangles are congruent.

**Theorem**

If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another triangle, then the two triangles are congruent.

**Proof**

Let and be right triangles right angled at and . Let and .

It is given that angle and .

Since and are right angles, (Can you see why?).

So, by ASA Congruence, .

Therefore, if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another triangle, then the two triangles are congruent.