阿Q吧 > 如图所示，已知AD是三角形ABC的角平分线，AD的垂直平分线交AB于点F，交BC的延长线于点E，连

如图所示，已知AD是三角形ABC的角平分线，AD的垂直平分线交AB于点F，交BC的延长线于点E，连

2025-03-16 23:50:04
推荐回答（1个）
回答1：

因为EF垂直评分AD
所以EA=ED
所以角EAD=角EDA

而角EAD=角EAC+角CAD
角EDA=角DAB+角B
所以角EAC+角CAD=角DAB+角B

因为AD是角BAC的角平分线
所以角CAD=角DAB

因此，我们得出：∠EAC=∠B

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