1 . 在如图所示的几何体中,正方形
与梯形
所在平面相交,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/1e3705cf-bc51-44b3-9be2-f4544ea1df1c.png?resizew=175)
(1)证明:
平面
;
(2)若
平面
,试求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d525d8b43670233010b604ddf383b4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c56903f8f497bc868ef67bd3d8593d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/1e3705cf-bc51-44b3-9be2-f4544ea1df1c.png?resizew=175)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
名校
2 . 设m,n是两条不同的直线,
,
是两个不同的平面,下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() | D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-10-27更新
|
528次组卷
|
2卷引用:山东省青岛市青岛第三十九中学2020-2021学年高三上学期期中数学试题
21-22高一下·浙江·期中
3 . 已知
是两条不同的直线,
,
是两个不重合的平面,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
4 . 如图,三棱柱
中侧棱与底面垂直,且AB=AC=2,AA1=4,AB⊥AC,M,N,P,D分别为CC1,BC,AB,
的中点.
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
您最近一年使用:0次
解题方法
5 . 已知两条直线
,两个平面
,给出下面四个命题:
①若
,
或者
相交;
②
,
,
;
③
,
;
④
,
或者
;
其中正确命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c166c4d75211e5294eb440bf2a6350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0966632633391af468776ec08a0f96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202af51f5ebe87ec0017f439a6ad7fbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcc6ebd43f5b10632cc8ba689c7cb3e.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a4c549e7ea8776ec821c467bc1a913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c748a85463206734745545a3c26388.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c166c4d75211e5294eb440bf2a6350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c748a85463206734745545a3c26388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d6ca6fed060a95127579051f7a6b79.png)
其中正确命题的序号是( )
A.①③ | B.②④ | C.①④ | D.②③ |
您最近一年使用:0次
2022-06-07更新
|
627次组卷
|
2卷引用:福建省安溪一中、养正中学、惠安一中、泉州实验中学2021-2022学年高一下学期期中数学试题
解题方法
6 . 如图所示,正方形ADEF与梯形ABCD所在的平面互相垂直,已知
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/73e79a0f-8581-4fa1-a9e6-d307229998c3.png?resizew=215)
(1)求证:
平面
;
(2)连接
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffda707068a4a1778e79da6f20fb86d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/73e79a0f-8581-4fa1-a9e6-d307229998c3.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
您最近一年使用:0次
2022-05-07更新
|
594次组卷
|
3卷引用:四川省成都市郫都区2021-2022学年高二下学期期中考试文科数学试题
名校
解题方法
7 . 已知点E,F分别是正方体ABCD-A1B1C1D1的棱AB,AA1的中点,点M,N分别是线段D1E与C1F上的点,则满足与平面ABCD平行的直线MN有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/838a0a72-4ca7-49f8-a02a-78df1653b2f4.png?resizew=161)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/838a0a72-4ca7-49f8-a02a-78df1653b2f4.png?resizew=161)
A.0条 | B.1条 | C.2条 | D.无数条 |
您最近一年使用:0次
2022-05-07更新
|
1198次组卷
|
16卷引用:江苏省星海2020-2021学年高一下学期期中数学试题
江苏省星海2020-2021学年高一下学期期中数学试题江苏省苏州市星海实验中学2020-2021学年高一下学期期中数学试题北京市中关村中学2021-2022学年高二上学期期中考试数学试题北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题2016届上海市松江区高三上学期期末质量监控(文)数学试题2016届上海市松江区高三上学期期末质量监控(理)数学试题2016届上海市松江区高考一模(文科)数学试题2016届上海市松江区高考一模(理科)数学试题2020届广西钦州市第三中学高三上学期理数考试题(已下线)课时42 空间平面与平面的位置关系-2022年高考数学一轮复习小题多维练(上海专用)北京市北京理工大学附属中学2021届高三12月月考数学试题(已下线)文科数学-2022年高考考前押题密卷(全国乙卷)(已下线)专题30 直线、平面平行的判定与性质-36.4.2平面与平面平行的性质 课时练习2020-2021学年高一下学期数学北师大版(2019)必修第二册4.4.1 平面与平面平行的性质(已下线)FHsx1225yl159
名校
8 . 如图,C,D分别是以AB为直径的半圆O上的点,满足
,△PAB为等边三角形,且与半圆O所成二面角的大小为90°,E为PA的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/3a73e84a-27cb-4df4-a354-5424ece967b6.png?resizew=138)
(1)求证:DE//平面PBC;
(2)求二面角A-BE-D的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e925392d0bf25a1a5c698ec1d8adea4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/3a73e84a-27cb-4df4-a354-5424ece967b6.png?resizew=138)
(1)求证:DE//平面PBC;
(2)求二面角A-BE-D的余弦值.
您最近一年使用:0次
2022-01-29更新
|
440次组卷
|
3卷引用:海南省洋浦中学2022-2023学年高二下学期期中数学试题
解题方法
9 . 已知
是矩形
所在平面外一点,
,
分别是
,
的中点,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/1d0ba465-f9e4-4567-a91a-5f1d7a49cd0d.png?resizew=199)
您最近一年使用:0次
真题
10 . 已知点
,
分别是正方形
的边
,
的中点.现将四边形
沿
折起,使二面角
为直二面角,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/41c45b60-a627-425c-b9bf-8a2262895c49.png?resizew=184)
(1)若点
,
分别是
,
的中点,求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41c2d7ae6aaf6d91129ed5221a415a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69856a547e733af483753a1dc51f47bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/41c45b60-a627-425c-b9bf-8a2262895c49.png?resizew=184)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b8c2721ada247b03f41f328539b301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41c2d7ae6aaf6d91129ed5221a415a7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
您最近一年使用:0次
2021-09-15更新
|
5925次组卷
|
7卷引用:广东省惠州市龙门县高级中学2021-2022学年高二下学期期中数学试题
广东省惠州市龙门县高级中学2021-2022学年高二下学期期中数学试题2020年山东省春季高考数学真题(已下线)考向23 点、直线、平面之间的位置关系-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)第11讲 直线与平面、平面与平面的位置关系-【寒假自学课】2022年高一数学寒假精品课(苏教版2019必修第二册)(已下线)专题20 立体几何综合大题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)(已下线)考向30 线线角、线面角、二面角与距离问题(四大经典题型)(已下线)专题8-4 非建系型:探索性平行与垂直证明及求角度