Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle.

Question

Philoid · Accepted Answer

Let ABCD is a parallelogram.

Since, DC||AB and DA is transversal.

∠A + ∠D = 180

∠A + ∠D = 90

∠PAD + ∠PDA = 90

∠APD = 90

∠SPQ = 90

Similarly, ∠PQR = 90, ∠QRS = 90

And ∠PSR = 90

Thus, PQRS is a quadrilateral each of whose angles is 90.

Hence, PQRS is a rectangle.