ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD.
F is the mid-point of BC.
BD intersected EF at G.
E is the mid point of AD and also EG || AB.
Thus, G is the mid point of BD (Converse of mid point theorem)
G is the mid point of BD and also GF || AB || DC.
Thus, F is the mid point of BC (Converse of mid point theorem)