We have to prove that the quadrilateral is a parallellogram.
We already know that one diagonal, EG, bisects the other diagonal FH, as J is the midpoint of FH..
The condition to be a parallelogram is that both diagonals bisect each other, so the additional information we need is that EJ is equal to JG, meaning that FH bisects EG.
Then, the additional information we need is EJ = GJ (Option B).