(a) In figure (1) given below, ABCD is a parallelogram and X is the mid-point of BC. The line AX
produced meets DC produced at Q. The parallelogram ABPQ is completed.
Prove that:
(i) the triangles ABX and QCX are congruent;
(ii)DC = CQ = QP
(b) In figure (2) given below, points P and Q have been taken on opposite sides AB and CD
respectively of a parallelogram ABCD such that AP = CQ. Show that AC and PQ bisect each
other.
