Proof: from the meaning of the question, d, e and f are the midpoint of BC AC AB respectively.

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