1 . 有一张矩形纸片
,按下面步骤进行折叠:
第一步:如图①,将矩形纸片
折叠,使点
,
重合,点
落在点
处,得折痕
;
第二步:如图②,将五边形
折叠,使
,
重合,得折痕
.再打开;
第三步:如图③,进一步折叠,使
,
均落在
上,点
,
落在点
处,点
,
落在点
处,得折痕
,
.
这样,就可以折出一个五边形
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/f542cf2b-0c93-4fa8-ac31-578892903940.png?resizew=141)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/669fd515-afbb-46a9-8023-86dc67d158c2.png?resizew=141)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/6c2b59a9-a749-4b81-9264-bd4b80f19283.png?resizew=141)
(1)适当添加辅助线,请写出图①中三组全等三角形______,______,______;(写出不同的三组即可)
(2)若这样折出的五边形
(如图③)恰好是一个正五边形,当
,
,
①请写出一个
与
的关系式,并加以证明;
②设正五边形的边长
,请求出边长
(用
或
表示
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
第一步:如图①,将矩形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
第二步:如图②,将五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8149f05bbaf25926ad9ac243a04b482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae72f1da4f5d540dc1e6f42ea08f952e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
第三步:如图③,进一步折叠,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae72f1da4f5d540dc1e6f42ea08f952e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b1a5427d8ff23df0f3ec194756c84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f6927cc2a930203ac34366383e76ef.png)
这样,就可以折出一个五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db24888830edd7df393bf95fde1281e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/f542cf2b-0c93-4fa8-ac31-578892903940.png?resizew=141)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/669fd515-afbb-46a9-8023-86dc67d158c2.png?resizew=141)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/16/6c2b59a9-a749-4b81-9264-bd4b80f19283.png?resizew=141)
(1)适当添加辅助线,请写出图①中三组全等三角形______,______,______;(写出不同的三组即可)
(2)若这样折出的五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db24888830edd7df393bf95fde1281e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c52b857c7ca55dfa6da108df1d3cee2.png)
①请写出一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
②设正五边形的边长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21350a49d9229ef239253f7c3d366ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2 . 在直角坐标系
中,经过点
,且关于
轴对称的曲线的方程是__________ .(填上正确的一个方程即可,不必考虑所有的情形)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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名校
3 . 在平面直角坐标系中有两点
,
,若二次函数
的图象与线段
只有一个交点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85dd382fa447b567a9de87cac1990d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302e421a250119f34d8f3c9928730490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae716e1168534de81763d2587257a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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