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人教版八年级数学经典几何题型展示

2013-10-08 16:28:58| 分类：八年级数学上 | 标签： |举报 |字号大中小订阅

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已知：在直角坐标系中，点A是y轴正半轴上一点，点B是x轴正半轴上一点，且OA=OB,点C是第一象限内的点，且AC垂直于BC,求∠ACO的度数。

解：过O作OM垂直于AC于M,作ON垂直于CB交延长线与N

在四边形OMCN中，∠OMC、∠ONC、∠MCN都是90°

∴∠MON=90°

又∠AOB=90°

∴∠AOM=∠BON

又∠OMA=∠ONB=90°

OA=OB

∴△OMA全等于△ONB

∴OM=ON

又OM⊥AC,ON⊥CN

∴O在∠ACB的平分线上

∴∠ACO=45°

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