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

In ΔACD,
S is mid-point to DA [∵ Given]
R is mid-point of DC [∵ Given]
Hence, SR ∥ AC and SR = (1/2)AC … (1) [∵ Mid-point Theorem]

In ΔACD,
P is mid-point of AB [∵ Given]
Q is mid-point of BC [∵ Given]
Hence, PQ ∥ AC and PQ = (1/2) AC …(2) [∵ Mid-Point Theorem]

From (1) and (2), we have
PQ ∥ SR …(3) [∵ PQ ∥ AC and SR ∥ AC]
and PQ = SR …(4) [∵ SR = (1/2)AC and PQ = (1/2)AC]
In quadrilateral PQRS,
PQ ∥ SR and PQ = SR [∵ From (3) and (4)]
Hence, PQRS is a parallelogram and diagonals of parallelogram bisect each other.
Therefore, SQ and PR bisects each other.