Pls answer question 51

We have the following situation-

Let ABCD be a quadrilateral and P,Q,R and S be the mid point of the respective sides of the triangle.

Since according to the mid point theorem, line joining the mid-points of two sides of the triangle is parallel to the third side and half of it.

In triangle ABC

$P Q = \frac{1}{2} A C P Q | | A C$

Similarly in triangle ADC

$R S = \frac{1}{2} A C R S | | A C$

Hence, opposite sides are equal and parallel.

$P Q = R S P Q | | R S \Rightarrow P Q R S i s a | | g m .$