And because AB=AC, isosceles triangle ABC.
So DE=EC DE//AB
So angle ACD= angle GDC GD//AB.
And because of FG//BE,
Parallelogram FBEG,
So EG=FB=DE=EC=AE.
So AC=GD
Because DC is on the public side,
So the triangle ACD is equal to the triangle GDC.
So AD=GC