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

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