如图,AB∥CD,E为AD上一点,且BE、CE分别平分∠ABC、∠BCD,求证:AE=ED.

问题描述:

如图,AB∥CD,E为AD上一点,且BE、CE分别平分∠ABC、∠BCD,求证:AE=ED.

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≌△...