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

If the angle of a quadrilateral are equal, prove that it is a rectangle.

Prove that each angle of a rectangle is 90°.