ABCD is a parallelogram in which E and F are midpoints of AD and BC respectively. BE intersects AF at G and FD intersects EC at H. Then GFHE is a _________.

 

 

Since ABCD is a parallelogram,

$\therefore$ AB = DC and AB$\parallel$DC

Also, AFCE and EBFD are parallelograms since opposite sides are equal and parallel,

In quadrilateral GFHE,

GF is a part of AF and EH is a part of EC

$\therefore$GF$\parallel$EH since AF$\parallel$EC

Similarly, GE is a part of BE and FH is a part of FD

$\therefore$GE$\parallel$FH since BE$\parallel$FD

Hence, GFHE is a parallelogram