OA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AED

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/27 00:40:20
OA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AEDOA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AEDOA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AED证法1:

OA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AED
OA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AED

OA=OB,OC=OD,∠AOB=∠COD,求证OE平分∠AED
证法1:
梅涅劳斯定理OA/AC×CE/EB×BD/DO=1
OA/OD=OB/OC BD=AC
所以OB/OC=EB/EC
符合角平分线定理逆定理,所以OE平分∠COD
证法2:
△OAD≌△OBC
∠C=∠D
又BD=AC,OC=OD
△OCE≌△ODE
搞定