Question

Let ABCD be a parallelogram and suppose the bisectors of ∠A and ∠B meet at P. Prove that ∠APB = 90°.

Answer 1

Given: Parallelogram ABCD, where the bisectors of angles A and B meet at P

To Prove:

Proof:

Since AP is the angle bisector of,.

Since BP is the angle bisector of,.

Since ABCD is a parallelogram, we get:

Now, in triangle APB, we have: