∴DC=BA,DC//BA,∠CDB=∠ABD

Points g and h are on the extension lines of BA and DC, respectively, and AG=CH.

∴DH=BG,∠HDB=∠GBD=∠CDB=∠ABD

BE = DF，∠HDB=∠GBD，BG=DH

∴△GBE≌△DHF

∴GE=HF,∠GEB=∠DFH

∴∠GEF=∠HFE

∴GE‖FH

∴GE=FH,GE‖FH

A quadrilateral with one side parallel and equal is a parallelogram.

∴ Quadrilateral GEHF is a parallelogram.