Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other

In △ABC, P and Q are mid- points of AB and BC respectively. Using mid point theorem PQ∥AC and PQ=1/2AC (1)
Similarly, RS∥AC and RS=1/2AC (2)
From (1) and (2)
Therefore, PQ∥SR and PQ=SR
Thus, a pair of opposite sides of a quadrilateral PQRS are parallel and equal.
Therefore, quadrilateral PQRS is a parallelogram.
Since the diagonals of a parallelogram bisect each other.
OP=OR and OQ=OS
Therefore, diagonals PR and QS of a parallelogram PQRS i.e., the line segments joining the mid- points of opposite sides of quadrilateral ABCD bisect each other.