Solutions; According to the problem, DC//AG, BD bisects the angle GBC and CD bisects the angle HCB.

Because DC//AG (known)

So angle FBD= angle CDB, angle DCB= angle CBA (two straight lines are parallel and the internal dislocation angles are equal).

Because BD bisects angle GBC and CD bisects angle HCB (known)

So GDB angle DCB angle BCA angle DCB angle.

So angle GDB= angle GBD, angle BCA= angle CBA (equivalent replacement)

So GD=GB, AB=AC (equilateral)

So AG=GD+AC

In this paper, two isosceles triangles are obtained by using the theorem that two straight lines are parallel and the internal dislocation angles are equal, and combining with the angle bisector, thus AG=GD+AC is obtained.