In a parallelogram, the diagonals bisect each other. Therefore, to find the segment that bisects EG in parallelogram DEFG, we need to identify which segment connects the vertices that are opposite and also intersects EG.
Since DEFG is a parallelogram, the diagonals DF and EG will bisect each other. This means that DF is the segment that bisects EG.
So, the correct answer is DF.