Prove that every diagonal of a rhombus bisects the angles at the vertices.

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

Prove that bisectors of any two opposite angles of a parallelogram are parallel.

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