F.3 Maths Properties of Quadrilaterals

Let AD=x, therefore AD=EN=PC=x (side of pararellogram).
Let ME=y, therefore BP=2y (by mid-point theorem).
Therefore MN=ME+EN=y+x
And BC=BP+PC=2y +x
And AD=x.
Therefore 2MN=2(x +y) =2x +2y=(2y+x) + (x)=BC+AD.

Using mid-point theorem

BF=2ME
FC=EN=AD

Now
AD+BC=AD+BF+FC=EN+2ME+EN=EN+ME+ME+EN=2MN

This like F.2 question.