Let ABCD be a quadrilateral, where P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively.Join PQ, QR, RS and SP.Let us also join PR, SQ and AC.Now, in ∆ABC, we have P and Q are the mid-points of its sides AB and BC respectively.∴PQ∥AC and PQ=21​AC…(1) [By mid-point theorem] Similarly, RS∥AC and RS=21​AC…(2) PQ || RS, PQ = RS∴ PQRS is a parallelogram.And the diagonals of a parallelogram bisect each other, i.e., PR and SQ bisect each other. Thus, the line segments joining the midpoints of opposite sides of a quadrilateral ABCD bisect each other.