ABCD is a quadrilateral
P,Q,R,S are mid points of sides AB,BC,CD and DA
In ∆ABC,
P and PQ are the mid points of AB and AC respectively
So, by using mid point theorem,
PQ || AC and PO = \(\frac{1}{2}\) AC ...(i)
Similarly,
In ∆BCD,
RS || AC and RS = \(\frac{1}{2}\) AC ... (ii)
From equation (i) and (ii)
PQ || RS and PQ = RS
Similarly, we have
PS || QR and PS = QR
Hence,
PQRS is a parallelogram.
Since,
Diagonals of a parallelogram bisects each other
Hence,
PR and QS bisect each other
Proved.