如图所示,在等边三角形
中,
平分
,点
为
边上一动点(与点
,
不重合),满足
,连接
.
(1)如图①所示,若
,
,求
.
(2)如图②所示,取
的中点
,连接
,
,
,探究线段
与
的位置与数量关系.
(3)如图③所示,把图②中的
绕点
顺时针旋转任意角度,然后连接
,点
为
的中点,连接
,
,
,问(2)中的结论还成立吗?若成立,请证明;若不成立,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa1aa5a7a5bb172ed4603f17c8b2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/2/eded27a6-550b-4717-bdaa-69fec8e8c46d.png?resizew=598)
(1)如图①所示,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5adaead91b4b6febfcdd6f995d81e550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3f1d2807be6d574e04ca9c6e721b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)如图②所示,取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(3)如图③所示,把图②中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
更新时间:2023-09-01 00:53:37
|
相似题推荐
解答题-问答题
|
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【推荐1】例题:有一个窗户形状如图1,上部是一个半圆,下部是一个矩形,如果制作窗框的材料总长为6
,如何设计这个窗户,使透光面积最大?这个例题的答案是:当窗户半圆的半径约为0.35
时,透光面积最大值约为1.05
.我们如果改变这个窗户的形状,上部改为由两个正方形组成的矩形,如图2,材料总长仍为6
,利用图3,解答下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/a6e7504d-b4cf-4782-a843-b3c041868660.png?resizew=320)
(1)若AB为1
,求此时窗户的透光面积?
(2)与课本中的例题比较,改变窗户形状后,窗户透光面积的最大值有没有变大?请通过计算说明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba007666deb89951641bd1e24bc174a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/14/a6e7504d-b4cf-4782-a843-b3c041868660.png?resizew=320)
(1)若AB为1
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
(2)与课本中的例题比较,改变窗户形状后,窗户透光面积的最大值有没有变大?请通过计算说明.
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解答题-作图题
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【推荐2】
是等边三角形,点
在
的延长线上,以
为中心,将线段
逆时针旋转
得线段
,连接
,
.
![](https://img.xkw.com/dksih/QBM/2022/6/17/3003467511963648/3006418690646016/STEM/d983b0ff119b434ebc9e260e3da5b6ba.png?resizew=509)
(1)如图
,若
,画出当
时的图形,并写出此时
的值;
(2)
为线段
的中点,连接
写出一个
的值,使得对于
延长线上任意一点
,总有
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d65a916cb6388b7bde4111910dcca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://img.xkw.com/dksih/QBM/2022/6/17/3003467511963648/3006418690646016/STEM/d983b0ff119b434ebc9e260e3da5b6ba.png?resizew=509)
(1)如图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2c9c32921b9f678056406dbb27fd9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39197c03fc84c8b56b98d318a3a1f366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b5dc06491b80897c68ab0f67b672ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40dcd98e38a4a265cb551138883c4b5.png)
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【推荐1】已知
、
.
(1)画出线段
,使A、B刚好是
的三等分点,C、A、B、D依次排列,请直接写出点C坐标______,点D坐标______;
(2)平移线段
,使A的对应点
刚好落在x轴上,B的对应点
刚好落在y轴上,在图上画出四边形
,并直接写出该四边形的面积为______;
(3)在(2)的条件下,若
交y轴于点
,直接写出线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49a31f8e8dba418bd5d886998ef8d17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/53cea7d0-c63e-4e6f-a271-a8cdd682b68f.png?resizew=170)
(1)画出线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)平移线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cf3a313649d7b92f28dd9fb8c27e41.png)
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【推荐2】如图①,一张矩形纸片
,其中
,
,先沿对角线
对折,点
落在点
的位置,
交
于点
.
(1)线段
与
是否相等?请说明理由;
(2)如图②,再折叠一次,使点
与点
重合,得折痕
,
交
于点
,求
和
长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6996aa31bf1486ced60c2249a6e6989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6747441b260ca043446b5d472fece440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e210795a966bd5dc1293479ab1988b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db94ea06ef27a92107d4bb70a404a826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/e41ff245-62c2-49d3-b1ac-42cc1c3216f8.png?resizew=285)
(1)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73d8ce7ee5d8676f7e8068c06765ddf.png)
(2)如图②,再折叠一次,使点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
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