In the adjoining figure, ABCD is a quadrilateral in which P, Q, R and S are midpoints of AB, BC, CD and DA respectively. AC is its diagonal. Show that

(i) SR || AC and SR = $\dfrac{1}{2}$AC

(ii) PQ = SR

(iii) PQRS is a parallelogram.

(i) In △ADC,

S and R are midpoints of AD and DC respectively,

∴ SR || AC and SR = $\dfrac{1}{2}$AC (By mid-point theorem) …..(i)

Hence, proved that SR || AC and SR = $\dfrac{1}{2}$AC (By mid-point theorem).

(ii) In △ABC,

P and Q are midpoints of AB and BC,

PQ || AC and PQ = $\dfrac{1}{2}$AC …….(ii)

Using (i) and (ii) we get,

PQ = SR and PQ || SR.

Hence, proved that PQ = SR.

(iii) Since, PQ = SR and PQ || SR.

Hence, proved that PQRS is a parallelogram.