triange

Hey there. The statement one tells us , that EG halves the the segment DF. Again, do not look at the picture as it is, abstract from it, you got just a triangle that might be iscoseles equilateral or none of these.
From stmt 1 we only know that DF is halved. (Vertice E may be to the left and to the right of the point where it stands at the picture)
we know nothing about a triangle, and about its angles.

stmt 2) gives us the measurement of angle EDF. still isufficient, other two angles can be whatever you wish.
1+2. We know one angle of the triangle, and that this triangle has a median which bisects the side DF. ( note , that ANY triangle has 3 medians that bisect a every side of a triangle, so it is nothing special about stmt 1.)
1+2 are still insufficient.

Answer is E.