ABCDE is a pentagon in which AB = AE, BC = ED and ∠ABC = ∠AED.

(a) Prove that :

(i) AC = AD

(ii) ∠BCD = ∠EDC

(b) If BC and ED are produced to meet at X, prove that BX = EX.

In the parallelogram ABCD, M is mid-point of AC and X, Y are points on AB and DC respectively such that AX = CY.

Prove that :

(i) triangle AXM is congruent to triangle CYM.

(ii) XMY is a straight line.

Construct a square ABCD in which each side = 5 cm.

Construct a square ABCD in which diagonal AC = 9 cm.