如图,在四边形ABCD中,AD平行BC,点E在边CD上,AE平分∠DAB,BE平分∠ABC,试说明:AD+BC=AB

如图,在四边形ABCD中,AD平行BC,点E在边CD上,AE平分∠DAB,BE平分∠ABC,试说明:AD+BC=AB

延长AE，交BC的延长线于点F∵AB‖CD∴∠DAB+∠B=180°∵E平分∠DAB，BE平分∠ABC∴∠AEB=90°∵∠F＝∠DAE=∠BAF∴AB=BF∵BE是∠ABF的平分线∴AF=EF易证△ADE≌△FCE∴AD=CF∴AB=BF=BC+CF=BC+AD

标签：AD,BC,平分