DF is the center line of right triangle ABD DF= 1/2AB.

FE is the center line of right triangle ABE EF= 1/2AB.

So DF=EF= 1/2AB.

So the triangle DFE is an isosceles triangle.

FG is perpendicular to DE, so FG is the center line.

The center line of an isosceles triangle bisects the vertex angle.

So Angel ·DFG = Angel ·EFG