In the adjoining figures, is a parallelogram in which the bisectors of and intersect at a point Prove that

Question

Philoid · Accepted Answer

ABCD is parallelogram.

We know that the sum of the adjacent angles in parallelogram is 180°

∴ ∠ A + ∠B = 180°

∴ + = = 90°

In ∆ APB, we have:
∠PAB = ∠A /2
∠PBA = ∠B /2
∴ ∠APB = 180 − (∠PAB + ∠PBA) …Angle sum property of triangle
∴ ∠APB = 180 – ( + )
∴ ∠APB = 180 − 90 = 90°
Hence, proved.