证明：作BE的延长线交CD的延长线于F，∵CE是∠BCD的平分线，∴∠BCE=∠FCE，∵AB∥CD，∴∠F=∠FBA，∵BE是∠ABC的平分线，∴∠ABF=∠FBC，∴∠FBC=∠F．在△FCE和△BCE中∠F＝∠FBC∠FCE＝∠BCECE＝CE，∴△FCE≌△...