Prove that the bisectors of the interior angles of a rectangle form a square.

In the given figure, ABCD is a parallelogram. Prove that : AB = 2BC.

Prove that the bisectors of interior angles of a parallelogram form a rectangle.

In the alongside figure, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B. Prove that :

(i) AQ = BP

(ii) PQ = CD

(iii) ABPQ is a parallelogram