In a parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that:

(i) AX = YC.

(ii) AX is parallel to YC

(iii) AXCY is a parallelogram.

The given figure shows a parallelogram ABCD. Points M and N lie in diagonal BD such that DM = BN. Prove that:

(i) △DMC ≅ △BNA and so CM = AN.

(ii) △AMD ≅ △CNB and so AM = CN.

(iii) ANCM is a parallelogram.

Use the information given in the following diagram to find the values of x, y and z.

The following figure is a rectangle in which x : y = 3 : 7; find the values of x and y.