Question

ABCD and AGFE are parallelograms with equal areas show that DG parallel FC

Answer 1

since the parallelograms are equal in area they lie between the same base and
between the same parallels
This brings to a point that one pair of the opposite sides of the made quadrilateral are parallels
and their corresponding angles are equal
so if one pair of opposite sides of a quadrilateral are parallel and their angles are equal it means
thier supplementary angles will also be equal
it means the other two pairs are also parallel
hence
DG parallels 
FC