∴AD‖BC, AB=CD (the opposite sides of a parallelogram are parallel and equal)

∴∠GBC=∠BGA, ∠BCE=∠CED (two straight lines are parallel with equal internal angles).

There are also ∵BG bisection ∠ABC, CE bisection ∠BCD (known),

∴∠ABG=∠GBC, ∠BCE=∠ECD (definition of angular bisector)

∴∠ABG=∠GBA,∠ECD=∠CED.

∴AB=AG, CE=DE (in the same triangle, equilateral)

∴AG=DE，

∴AG-EG=DE-EG, namely AE = DG.