如图,
,
,
,
交于点
,过点
作
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c9b20332-8c09-4b30-a642-be02fd3990be.png?resizew=195)
(1)求证:
;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3948450b1091640e5d34943eb05f405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178e3fa2e4de57a4c067e79be7d798e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/c9b20332-8c09-4b30-a642-be02fd3990be.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fca3734de79f7f50b552ef62b29dc7c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb6823a329628699619a39cde927510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
更新时间:2024-02-18 11:57:33
|
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解答题-证明题
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名校
【推荐1】已知,如图A、F、C、D四点在一直线上,AF=CD,AB//DE,且AB=DE,求证:
![](https://img.xkw.com/dksih/QBM/2011/12/14/1573304549556224/1573304564793344/STEM/bb5c230ccc344075b01f2e8430b9be9b.png?resizew=152)
(1)△ABC≌△DEF
(2)∠CBF=∠FEC
![](https://img.xkw.com/dksih/QBM/2011/12/14/1573304549556224/1573304564793344/STEM/bb5c230ccc344075b01f2e8430b9be9b.png?resizew=152)
(1)△ABC≌△DEF
(2)∠CBF=∠FEC
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【推荐2】如图,已知
,
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532aece6cfd67e2a97977eed978dbf2b.png)
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【推荐2】如图,BD,CE是△ABC的高,BD,CE相交于点F,BE=CD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/1a617ec5-84c6-49c8-9a03-756aaf61b968.png?resizew=149)
求证:
(1)Rt△BCE
Rt△CBD;
(2)AF平分∠BAC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/1a617ec5-84c6-49c8-9a03-756aaf61b968.png?resizew=149)
求证:
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(2)AF平分∠BAC.
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【推荐1】如图,以
的顶点
为圆心,适当长为半径画弧,与射线
,
分别交于点
,
,再分别以
,
为圆心,以大于
的长为半径画弧,两弧在
的内部交于点
,画射线
,过点
作MN
OB,交
于点
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/2a87dbc4-e20f-434e-9b9b-f2bd5962baad.png?resizew=141)
(1)射线
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(2)证明:
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/2a87dbc4-e20f-434e-9b9b-f2bd5962baad.png?resizew=141)
(1)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76dc356c599be3c35367d3566e038796.png)
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【推荐2】如图1,△ABC中,点O是AC边上的一个动点,过点O作直线
,设MN交∠BCA的平分线于点E,交∠DCA的平分线于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/05fe13f1-051e-4a06-b503-224fc1617471.png?resizew=321)
(1)线段CE与CF的位置关系是 ;
(2)探究:线段OE与OF的数量关系,并加以证明;
(3)如图2,当点O运动到何处时,四边形AECF是矩形,并说明理由;
(4)在(3)的前提下,直接写出△ABC满足什么条件时,四边形AECF是正方形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1dc52a8ba9f389800eb92dbd145bf5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/05fe13f1-051e-4a06-b503-224fc1617471.png?resizew=321)
(1)线段CE与CF的位置关系是 ;
(2)探究:线段OE与OF的数量关系,并加以证明;
(3)如图2,当点O运动到何处时,四边形AECF是矩形,并说明理由;
(4)在(3)的前提下,直接写出△ABC满足什么条件时,四边形AECF是正方形.
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