AB=AC,BE和CD是∠ABC和∠ACB的平分线,说明DO=EO

题目

AB=AC,BE和CD是∠ABC和∠ACB的平分线,说明DO=EO

答案

AB=AC,BE和CD是∠ABC和∠ACB的平分线,BE、CD相交于O,说明DO=EO
AB=AC =>∠DBC=∠ECB；BE和CD是∠ABC和∠ACB的平分线 =>∠EBC=1/2∠DBC、∠DCB=1/2∠ECB；∴∠EBC=∠DCB =>∠OBC=∠OCB =>OC=OB ----(1)
在ΔBCD和ΔCBE中：∠DBC=∠ECB、BC=CB、∠EBC=∠DCB ∴ΔBCD≌ΔCBE =>DC=EB --(2)
(2)-(1)得：DO=EO