<Tri-2025-2234>, hint

Consider coordinate system :

Let B(0,0), D(1,1), BE=t, then  

DF; y=(1-t)x+t,  CE ; y=-tx+t, AF; y={(1-t)/t}x+1.

Calculation shows BG is perpendicular to DF . (1-t) X{1/(t-1)}=-1.