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> 在△ABC中,∠C=90°,AB=2AC,AD为∠BAC的平分线,求证:D在AB的垂直平分线上。-八年级数学
在△ABC中,∠C=90°,AB=2AC,AD为∠BAC的平分线,求证:D在AB的垂直平分线上。-八年级数学
题目简介
在△ABC中,∠C=90°,AB=2AC,AD为∠BAC的平分线,求证:D在AB的垂直平分线上。-八年级数学
题目详情
在△ABC中,∠C=90°,AB=2AC,AD为∠BAC的平分线,求证:D在AB的垂直平分线上。
题型:证明题
难度:中档
来源:同步题
答案
证明:∵在△ABC 中,∠C=90°,AB=2AC ,
∴∠BAC=60°,∠ABC=30°
∵AD 平分∠BAC,
∴∠BAD=30°
∴∠BAD=∠ABC
∴BD=AD
∴D在AB的垂直平分线上。
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题目简介
在△ABC中,∠C=90°,AB=2AC,AD为∠BAC的平分线,求证:D在AB的垂直平分线上。-八年级数学
题目详情
答案
∴∠BAC=60°,∠ABC=30°
∵AD 平分∠BAC,
∴∠BAD=30°
∴∠BAD=∠ABC
∴BD=AD
∴D在AB的垂直平分线上。