Question

The Hypotenuse Angle Theorem, similar to the HL Theorem, states that if the hypotenuse and one angle of a right triangle are congruent to the hypotenuse and corresponding angle of another right triangle then the triangles are congruent. Prove the HA theorem

Answer 1

Step-by-step explanation:

In order to proof the HA theorem, we consider two triangles  and   which are right angle triangles. The right angle lies at points  and   respectively.

We also consider that the hypotenuse are congruent meaning  and  .

Now we have taken that angle  and  .

Since  and  are 90 degrees, so angle B would be congruent to angle E i.e  

Hence by Angle, side and angle congruence in both triangles we can write as,  .

And this is what the HA thoerem states also