1 . 如图,已知正方体
的棱长为2,点E,F,G,H,I分别为线段
,
,
,BC,
的中点,连接
,
,
,DE,BF,CI,EH,则下列正确结论的序号是______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/27/ecb2fd98-bc9d-4491-97e3-678b2656b30b.png?resizew=156)
①点E,F,G,H在同一个平面上;
②直线DE,BF,CI交于同一点;
③直线BF与直线
所成角的余弦值为
;
④该正方体过EH的截面的面积最大值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/27/ecb2fd98-bc9d-4491-97e3-678b2656b30b.png?resizew=156)
①点E,F,G,H在同一个平面上;
②直线DE,BF,CI交于同一点;
③直线BF与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
④该正方体过EH的截面的面积最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
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