如图,在正三棱柱
中,已知D,E分别为BC,
的中点,点F在棱
上,且
.求证:
(1)直线
平面
;
(2)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08450c427df8de7e302ad41a2902ca9f.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d560542b646924eaf577480ac73281b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004dd8ad9e5a200b3869ebfc59c2446d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
![](https://img.xkw.com/dksih/QBM/2019/4/26/2190821785329664/2191021648756736/STEM/852113b1033d41f9a870e89b3a812adf.png?resizew=149)
更新时间:2016-12-05 01:36:37
|
相似题推荐
解答题-证明题
|
较易
(0.85)
【推荐1】如图,直三棱柱
的底面为直角三角形且
,直角边
、
的长分别为3、4,侧棱
的长为4,点M、N分别为线段
、
的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877450336092160/2878770239651840/STEM/c3abc82d-9f0c-4eba-9328-e22fb2525a1c.png?resizew=269)
(1)求证:A,C,N,M四点共面;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35850dbc661ded6456b70767cc6cd0.png)
![](https://img.xkw.com/dksih/QBM/2021/12/21/2877450336092160/2878770239651840/STEM/c3abc82d-9f0c-4eba-9328-e22fb2525a1c.png?resizew=269)
(1)求证:A,C,N,M四点共面;
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e22545a765af9563ea7c8db75c16df6.png)
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【推荐2】已知直三棱柱
的所有棱长都相等,且
分别为
的中点.
(1)求证:平面
平面
;
(2)求证:平面C
平面
.
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/6214afffe72a4ee2a4dbf338825645b8.png)
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/1ca08597c3ae488696459a103b2308c6.png)
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/7befce2a1ed44e3697d12279d5afd8bc.png)
(1)求证:平面
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/edb4996fd1af468f9f8297ab63e499fc.png)
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/286efa58067a4b57b126682de4ab189f.png)
(2)求证:平面C
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/08af346f94454157a236c529b95a99e2.png)
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/286efa58067a4b57b126682de4ab189f.png)
![](https://img.xkw.com/dksih/QBM/2015/12/18/1572370224627712/1572370230820864/STEM/ea42fda7dec645fa84b176f9be8645bc.png)
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解答题-问答题
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较易
(0.85)
【推荐1】如图,四棱锥
中,
,
,
,
,侧面
为等边三角形.
![](https://img.xkw.com/dksih/QBM/2016/8/24/1572989027606528/1572989033758720/STEM/ca99492070a945e6b67f820290d45cd8.png)
(1)证明:
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aa0d36da718de7c50a781b8e2bb8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe769bb9c0c0b9ab500f925e77710941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578b8b2e929abc6e2fb4843cfb63e5a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://img.xkw.com/dksih/QBM/2016/8/24/1572989027606528/1572989033758720/STEM/ca99492070a945e6b67f820290d45cd8.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fd722fb39ff555af13c678ac683477.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882c90e28b53511601de1f63cb7ec2c0.png)
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解题方法
【推荐2】在正方体
中,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442beba7ef17d73029f5aeff3d944c04.png)
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