ABCD is a square. E, F, G and H are points on the sides AB, BC, CD and DA respectively such that AE = BF = CG = DH. Prove that EFGH is a square.

ABCD is a square and the diagonals intersect at O. If P is a point on AB such that AO = AP, prove that 3∠POB = ∠AOP.

In the figure (1) given below, ABCD and ABEF are parallelograms. Prove that

(i) CDFE is a parallelogram.

(ii) FD = EC

(iii) △AFD ≅ △BEC.

In the figure (2) given below, ABCD is a parallelogram, ADEF and AGHB are two squares. Prove that FG = AC.