In given figure ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that: SR∥AC and SR=1/2AC

(i) In ΔACD, we have S is the mid-point of AD and R is the mid- point of CD. Then SR∥AC. Using Mid point theorem SR=1/2AC
(ii) In ΔABC, P is the mid-point of the side AB and Q is the mid-point of the side BC. Then, PQ∥AC and using Mid point Theorem PQ=1/2AC
Thus, we have proved that : PQ∥AC and SR∥AC ⇒PQ∥SR
Also PQ=SR=1/2AC
(iii) Since PQ=SR and PQ∥SR. One pair of opposite sides are equal and parallel. ⇒PQRS is a parallelogram.