名校
1 . 已知正方体
的边长为2,点E,F分别是线段
,
的中点,平面
过点
,E,F,且与正方体
形成一个截面,现有如下说法:
①截面图形是一个六边形;
②棱
与平面
的交点是
的中点;
③若点I在正方形
内(含边界位置),且
,则点
的轨迹长度为
;
④截面图形的周长为
;
则上述说法正确的命题序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
①截面图形是一个六边形;
②棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
③若点I在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786178c4141686b703850e72f87d12ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6836c9e3e3001df21030fbda3802b15.png)
④截面图形的周长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29587f681356659028a787bffa098417.png)
则上述说法正确的命题序号为
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2021-11-06更新
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6卷引用:湖南省永州市第二十八中学2021-2022学年高一下学期期中数学试题