ABCD is a parallelogram. If AB = 2AD and P is the mid-point of CD; prove that : ∠APB = 90°.

Construct a parallelogram ABCD in which diagonal AC = 6.3 cm; diagonal BD = 7cm and the acute angles between the diagonals is 45°.

In a parallelogram ABCD, P is a point on side AD such that 3AP = AD and Q is a point on BC such that 3CQ = BC. Prove that : AQCP is a parallelogram.

The following figure shows a parallelogram ABCD.

Use the given informations to find the values of x, y and z.