So the triangle AED is equal to AGD.
So DE=DG? Angle 4= angle AGD
So the angle 1= angle 2 (1)
Because angle EDF plus angle EAF is equal to 180.
So angle 3+ angle 4 = 180.
Because angle 1+ angle 4 = 180.
So angle 1= angle 3 (2)
From (1)(2):
Angle 2= Angle 3
So DF=DG
So DE=DF