Question

ABCD is a quadrilateral in which P.Q,R and S are mid-points of the sides AB, BC,CD and DA ( see the given figure). AC is a diagonal. It can be concluded that PQ = SR

• A. True
• B. False

Answer 1

The correct option is A True

In $\Delta$ABC, P and Q are mid - points of sides AB and BC respectively. Therefore, by using mid-point theorem,
PQ || AC and PQ = $\frac{1}{2}$AC .........(2)
Using equations (1) and (2) , we obtain
PQ || SR and PQ = SR …..(3)
$\therefore$ PQ = SR