And AE=BF=AB.

∴AF=AD

Angle F= angle ADF

∵ Quadrilateral ABCD is a parallelogram

∴AB//CD,AD//BC (the opposite sides of a parallelogram are parallel)

Namely AF//DC

∴ Angle F= Angle FDC, Angle ADC+ Angle BCD = 180.

∴ Angle F= 1/2 Angle ADC

Same angle E= 1/2∠BCD

∴∠E+∠F= 1/2(∠ADC+∠BCD)=90

∠∠E+∠F+∠EGF = 180

∴∠EGF=90 EC⊥FD