Question

如图,△ABC中,AB=AC,BE,CD是角平分线,则BD=CE,请说明理由

Answer 1

∵AB=AC,∴∠ABC=∠ACB,

∵BE、CD分别平分∠ABC、∠ACB,

∴∠ABE=1/2∠ABC,∠ACD=1/2∠ACB,

∴∠ABE=∠ACD,

在ΔABE与ΔACD中,

∠ABE=∠ACD,

AB=AC,

∠A=∠A,

∴ΔABE≌ΔACD,

∴AD=AE,

∴AB-AD=AC-AE,

即BD=CE.