题型:解答题-证明题
难度:0.65
引用次数:1423
题号:9100180
阅读下面材料,并解决问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/1f4ef2b6-867b-498e-b22c-53760685bfb0.png?resizew=524)
(1)如图①等边△ABC内有一点P,若点P到顶点A、B、C的距离分别为3,4,5,求∠APB的度数.
为了解决本题,我们可以将△ABP绕顶点A旋转到△ACP′处,此时△ACP′≌△ABP,这样就可以利用旋转变换,将三条线段PA、PB、PC转化到一个三角形中,从而求出∠APB=__________;
(2)基本运用
请你利用第(1)题的解答思想方法,解答下面问题:
已知如图②,△ABC中,∠CAB=90°,AB=AC,E、F为BC上的点且∠EAF=45°,求证:EF2=BE2+FC2;
(3)能力提升
如图③,在Rt△ABC中,∠C=90°,AC=1,∠ABC=30°,点O为Rt△ABC内一点,连接AO,BO,CO,且∠AOC=∠COB=∠BOA=120°,求OA+OB+OC的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/1f4ef2b6-867b-498e-b22c-53760685bfb0.png?resizew=524)
(1)如图①等边△ABC内有一点P,若点P到顶点A、B、C的距离分别为3,4,5,求∠APB的度数.
为了解决本题,我们可以将△ABP绕顶点A旋转到△ACP′处,此时△ACP′≌△ABP,这样就可以利用旋转变换,将三条线段PA、PB、PC转化到一个三角形中,从而求出∠APB=__________;
(2)基本运用
请你利用第(1)题的解答思想方法,解答下面问题:
已知如图②,△ABC中,∠CAB=90°,AB=AC,E、F为BC上的点且∠EAF=45°,求证:EF2=BE2+FC2;
(3)能力提升
如图③,在Rt△ABC中,∠C=90°,AC=1,∠ABC=30°,点O为Rt△ABC内一点,连接AO,BO,CO,且∠AOC=∠COB=∠BOA=120°,求OA+OB+OC的值.
更新时间:2019-12-05 15:07:56
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【推荐1】如图,
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(2)如图
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、
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(3)如图
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(1)如图
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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(2)如图
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解答题-问答题
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适中
(0.65)
【推荐2】在
中,
,点O为
边的中点,连接
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(1)如图1,当
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与
的数量关系__________
(2)如图2,延长
到点D,使
,连接
,若
.
①求
的值;
②求
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(2)如图2,延长
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②求
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名校
【推荐1】在平面直角坐标系中,已知点A在第一象限,点B在y轴的正半轴上
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【推荐2】已知:在四边形
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解答题-问答题
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【推荐1】在四边形
中,
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【推荐2】
中,
,垂足为E,连接
,将
绕点E逆时针旋转
得到
,连接
.
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(1)当点E在线段
上,
时,如图①,求证:
:
(2)当点E在线段
延长线上,
时,如图②;当点E在线段
延长线上,
时,如图③,请猜想并直接写出线段
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(3)在(1)、(2)的条件下,若
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______.
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(1)当点E在线段
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42ed2e5bd5a0f033e24008697bf4963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d622735249092bf5702e51fc4428044.png)
(2)当点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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