Prove that bisectors of any two adjacent angles of a parallelogram are at right angles.

If the diagonals of a quadrilateral are equal and bisect each other at right angles, then prove that it is a square.

ABCD is a parallelogram. If the diagonal AC bisects ∠A, then prove that :

(i) AC bisects ∠C

(ii) ABCD is a rhombus

(iii) AC ⊥ BD

If ABCD is a rectangle in which the diagonal BD bisects ∠B, then show that ABCD is a square.