1 . 如图,直三棱柱
,
,
点M,N分别为
和
的中点.
(Ⅰ)证明:
∥平面
;
(Ⅱ)若二面角
为直二面角,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d8fd172a3638b435e758f2bf40e2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e737bc35da650eda3825d29799b5f86f.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06faea49d957a5bab3fe0582f76ff23.png)
(Ⅱ)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca78edfd819b3b675455e9f7897f0d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://img.xkw.com/dksih/QBM/2012/7/5/1570916308729856/1570916314087424/STEM/fe8797518c5d4106a830946620f8440a.png?resizew=265)
您最近一年使用:0次
2019-01-30更新
|
1677次组卷
|
3卷引用:2012年全国普通高等学校招生统一考试理科数学(辽宁卷)
2012年全国普通高等学校招生统一考试理科数学(辽宁卷)(已下线)2013届陕西省西安市西北工业大学附中高三第十二次适应性训练理数学卷江苏省南通市如皋市部分学校2021届高三下学期6月份临门一脚考试数学试题
真题
2 . 如图所示,在多面体
,四边形
,
均为正方形,
为
的中点,过
的平面交
于F.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/e883898c-6ebd-4d8d-97d2-84bee297e78d.jpg?resizew=147)
(Ⅰ)证明:
;
(Ⅱ)求二面角
余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b6e1ec79fd5adf04c8a98df0745e26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc0275012259c2bc7c8c3a59448b0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53de67d55ead2f0347f902e6f9d5da42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/e883898c-6ebd-4d8d-97d2-84bee297e78d.jpg?resizew=147)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce20c644ba87698752ab4e72d4abca0.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165d8a626561c01210793e42859f7ed0.png)
您最近一年使用:0次
2016-12-03更新
|
2646次组卷
|
7卷引用:2015年全国普通高等学校招生统一考试理科数学(安徽卷)
2015年全国普通高等学校招生统一考试理科数学(安徽卷)(已下线)专题47 空间向量与立体几何专题训练-2021年高考一轮数学(理)单元复习一遍过(已下线)专题47 空间向量与立体几何专题训练-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)1.4.2 用空间向量研究距离、夹角问题(分层练习)-2021-2022学年高二数学教材配套学案+课件+练习(人教A版2019选择性必修第一册)(已下线)2.4.4 向量与距离湘教版(2019)选择性必修第二册课本习题 习题2.4(已下线)专题23 立体几何解答题(理科)-2
3 . 如图,四棱锥
中,
⊥平面
,
∥
,
,
分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/f18faa4e-2cf7-4ee5-9181-54baf3a56cea.png?resizew=177)
(1)求证:
∥平面
;
(2)求证:
⊥平面
.
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/99b7365bd38e454b99fdf153507576d7.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/b2fc8f4fd7ce410da8f8e36fbc222d77.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/eec841c6bc1346c688b6d5f39711f4c5.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/21b5f6f4ee9e4319a8249156a8f87a2a.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/e4bb5abfaed94c828d4d19e4c9232843.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/1becfaf6cd0342ea9de181fc357a5d45.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/225b48eed600446c865aeb5b4818b29d.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/d35bf2eae1bd4b8381a27bd4c901ff91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/f18faa4e-2cf7-4ee5-9181-54baf3a56cea.png?resizew=177)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/b2fc8f4fd7ce410da8f8e36fbc222d77.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/b8c8347e93884e7b8b33b74e6e47de6d.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/8e8aa4665d044f798086a649095e33db.png)
![](https://img.xkw.com/dksih/QBM/2014/6/23/1578327850901504/1578327851425792/STEM/023fb000f09f47629573fec0612f57a7.png)
您最近一年使用:0次
2016-12-12更新
|
4822次组卷
|
3卷引用:2014年全国普通高等学校招生统一考试文科数学(山东卷)
4 . 如图,四棱锥
的底面
是平行四边形,
,
,
分别是棱
的中点.
(1)证明
平面
;
(2)若二面角P-AD-B为
,
①证明:平面PBC⊥平面ABCD
②求直线EF与平面PBC所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/fcd1b7fc31624ff385ea52a4702db72b.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/cf2e8de8f47442cdb01c12f1b394e7cb.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/0ee7d092f169443a98848f1c6b9ff5fd.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/3ec78dc2d0b9473bb9bc88b2e71be9a9.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/3c42684f74aa45c9a343400b7f7c3cac.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/f7395f98d94448e68ddc2cd5c5676e67.png)
(1)证明
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/55bde3f85e4143ce8b76237b6926e06a.png)
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/062ba29446934fbf876b29f1cb011f5f.png)
(2)若二面角P-AD-B为
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/3ad64abcfa59403e806ca3391d82baaa.png)
①证明:平面PBC⊥平面ABCD
②求直线EF与平面PBC所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2014/6/20/1571786659823616/1571786665459712/STEM/8b660d15-6a23-421e-be21-c097d68f75c0.png?resizew=248)
您最近一年使用:0次
真题
解题方法
5 . 已知空间四边形
中
,M,N,P,Q分别是边
的中点(如图).求证:
是一个矩形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0f6ef719c80878318cd86e95ef8cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a337a934b801730321f67b0e5a0b144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/d4cba854-c4ea-4f7a-bf78-9d9f248d3b05.png?resizew=135)
您最近一年使用:0次