AD是△ABC的中线,过DC上任意一点F,作EGǁAB,与AC和AD的延长线分别交...答:∵FG//AB,∴FG/AB=CF/BC,2FG/AB=2CF/BC.∵BC=2BD,∴2FG/AB=CF/BD 故 (EF+2FG)/AB=(DF+CF)/BD.∵DF+CF=CD=BD,∴EF+2FG=AB,EF+FG=AB-FG.∵FH//AC, EG//AB,∴AHFG为平行四边形,AH=FG.故 EF+FG=AB-AH,即EG=BH.而 EG//BH,∴ BEGH为平行四边形,∴ BE=GH ...