Question

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

Answer 1

Point A is common to both the parallelograms
both the parallelograms have equal area(base*height)
now if a transverse cut two parallel lines their alternate angles are equal
Join GD and FC
angle(GDA)=angle(DAC) 
which are alternate angles and AD is transverse to the lines GD and FC
=>GD is parallel to FC  

proved