∵af=bf,be=ce∴ef= 1/2ac,ef∥ac

∫AG = GH = HC = 1/3AC

∴EF/GC=3/4,GH/EF=2/3

∫EF∨GC

∴MF/MG=ME/MC=EF/GC=3/4

∴MF=3FG，ME=3EC

∴MB=2EC=2EB=BC

∫GH∨EF

∴DG/DF=GH/EF=2/3

∴DG=2FG，DF=3FG

∴MF=DF

* AFD =∠BFM

∴⊿AFD≌⊿BFM

∴∠DAF=∠MBF，AD=BM

∴AD∥BC, AD = BC

∴ quadrilateral ABCD is a parallelogram

Hope to adopt