解题方法
1 . 已知在直三棱柱
中,
,且
分别是
,
的中点.证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667661dd4aba3a7564b286fda89f4491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,底面
为菱形,
,又
底面
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/11/13/3108808518459392/3110391415267328/STEM/86761023ad4647bcaea4ca6a2685f20d.png?resizew=247)
(1)求证:
;
(2)设
是
的中点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d11e19c84255eb0431415c2dec553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2022/11/13/3108808518459392/3110391415267328/STEM/86761023ad4647bcaea4ca6a2685f20d.png?resizew=247)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37c9f2fec8e6966125547af2628d9bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
您最近一年使用:0次
2022-11-15更新
|
1289次组卷
|
5卷引用:江苏省苏州市2020-2021学年高一下学期期末数学试题
江苏省苏州市2020-2021学年高一下学期期末数学试题(已下线)8.6.1 空间直线、平面的垂直(精练)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)第29讲 线面垂直证线线平行和垂直2种题型(已下线)必修第二册期末测试卷(基础卷)山东省枣庄市枣庄市第八中学2023年高一下学期6月月考数学试题
名校
解题方法
3 . 如图①所示,已知正三角形
与正方形
,将
沿
翻折至
所在的位置,连接
,
,得到如图②所示的四棱锥.已知
,
,
为
上一点,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/0d855ffa-0ab1-4d06-900f-8e584e0b373d.png?resizew=259)
(1)求证:
平面
;
(2)在线段
上是否存在一点
,使得
平面
.若存在,指出点
的位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3736237f7bc84fc30f0bd75d5bba9242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad895b1c422b40c35be89c8bef22e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2c39a3d57d2de07a21550fe138ff77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6117f4a30d930911d33698444e8527f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bd11c1ac25b222f9613428412090a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/0d855ffa-0ab1-4d06-900f-8e584e0b373d.png?resizew=259)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eef01d240d3674e0113d1064569bce.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc063cdcf722f07a1aa57be04edd416d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d987bcf7114c002843702100444da017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea3cebae1762106ecd2a4fd56d07763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2023-04-19更新
|
575次组卷
|
4卷引用:13.2 基本图形位置关系(分层练习)
(已下线)13.2 基本图形位置关系(分层练习)浙江省宁波市北仑中学2022-2023学年高一下学期期中数学试题(已下线)立体几何专题:立体几何探索性问题的8种考法黑龙江省齐齐哈尔市第八中学校2022-2023学年高一下学期期末数学试题
名校
4 . 在如图所示的圆柱
中,AB为圆
的直径,
是
的两个三等分点,EA,FC,GB都是圆柱
的母线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/d8007de3-faa6-44e8-be88-ce79dcdd3739.png?resizew=192)
(1)求证:
平面ADE;
(2)设BC=1,已知直线AF与平面ACB所成的角为30°,求二面角A—FB—C的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/d8007de3-faa6-44e8-be88-ce79dcdd3739.png?resizew=192)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3d34e4702615fa0e908eda9440c93c.png)
(2)设BC=1,已知直线AF与平面ACB所成的角为30°,求二面角A—FB—C的余弦值.
您最近一年使用:0次
2020-06-29更新
|
2606次组卷
|
10卷引用:江苏省盐城中学2021届高三下学期仿真模拟数学试题
江苏省盐城中学2021届高三下学期仿真模拟数学试题山东省滨州市2020届高三三模考试数学试题(已下线)专题九 立体几何与空间向量-山东省2020二模汇编湖南省长沙市长郡中学2020-2021学年高三上学期月考(三)数学试题山西省怀仁市2020-2021学年高二上学期期中数学(理)试题湖南省岳阳市第一中学2020-2021学年高二下学期第一次质量检测数学试题江西省宜春市天立高级中学2020-2021学年高一下学期期末数学试题四川省巴中市恩阳区2021-2022学年高二上学期期中考试数学试题广东省佛山市南海区、三水区2023届高三上学期8月摸底数学试题四川省宜宾市叙州区第一中学校2022-2023学年高二上学期期中考试数学(理)试题
名校
5 . 如图,正方形
和直角梯形
所在平面互相垂直,
,
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/5196057a-6554-4001-8019-85ac67b33f8b.png?resizew=123)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ea9d3df7c2bcdf135dedd1554fb82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce38d8a8a7043586aad206f8153d0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a77f26a7be722e00baa984f769ec8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce84f6062f12bf6ef42d7b733cd2248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/7/5196057a-6554-4001-8019-85ac67b33f8b.png?resizew=123)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc521258fcaeaf7acffc5ae98c3af6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646084b7f3902efa4c462ed67599265a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a34e44c5d7e1d22521fb293994f5b0.png)
您最近一年使用:0次
2022-09-06更新
|
1015次组卷
|
6卷引用:江苏省淮安市盱眙县马坝高级中学2023-2024学年高三上学期期中数学试卷
名校
6 . 如图,多面体ABCDEF中,四边形ABCD为矩形,二面角A-CD-F为60°,
,CD⊥DE,AD=2,DE=DC=3,CF=6.
平面ADE;
(2)求直线AC与平面CDEF所成角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b0c41f8695cc909dd9395ef0726cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f2eae3483395cc6aca5160c64f83eb.png)
(2)求直线AC与平面CDEF所成角的正弦值
您最近一年使用:0次
2023-08-11更新
|
417次组卷
|
7卷引用:江苏省泰州市姜堰中学2020-2021学年高二下学期期末学情调测数学试题
江苏省泰州市姜堰中学2020-2021学年高二下学期期末学情调测数学试题湖南省岳阳市岳阳县第一中学2019-2020学年高二下学期期中数学试题重庆市蜀都中学2020-2021学年高二上学期12月月考数学试题山东省菏泽市鄄城县鄄城县第一中学2022-2023学年高一下学期5月月考数学试题(已下线)专题突破卷19传统方法求夹角及距离-1(已下线)专题05 直线与平面的夹角4种常见考法归类-【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)(已下线)第六章立体几何初步章末二十种常考题型归类(2)-【帮课堂】(北师大版2019必修第二册)
7 . 在矩形
中,AB=4,AD=2.点
分别在
上,且AE=2,CF=1.沿
将四边形
翻折至四边形
,点
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/4115fbbd-04cb-4551-9270-cb6e465c5275.png?resizew=396)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ba89e83329983cfadbfcdda151aaa3.png)
平面
;
(2)求异面直线
与
所成的角;
(3)在翻折的过程中,设二面角
的平面角为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c16d99496d31ce4d87301a4793393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c76e6c67644b8bad9bfe11c7ec3081d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7829855159327b2a87c3a424b3f7134a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/4115fbbd-04cb-4551-9270-cb6e465c5275.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ba89e83329983cfadbfcdda151aaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b12cffc313a181f666e3fc8e66b6f59.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
(3)在翻折的过程中,设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b43ff5a9a70210b4017c4c38b4258c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
解题方法
8 . 如图,在长方体
中,E,M,N分别是
的中点,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1142fad64ce162314e60c741b376f041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aca256a2888582d7691ce62453a49bc.png)
您最近一年使用:0次
2023-08-12更新
|
388次组卷
|
5卷引用:13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)
(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)人教B版(2019) 必修第四册 逆袭之路 第十一章 立体几何初步 11.3.3 平面与平面平行河南省郑州励德双语学校2022-2023学年高一下学期期中考试数学试题(已下线)8.5空间直线、平面的平行——课堂例题(已下线)8.5.3 平面与平面平行-同步精品课堂(人教A版2019必修第二册)
2023高二·全国·专题练习
9 . 直四棱柱
,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
平面
;
(2)若四棱柱体积为36,求二面角
大小的正切值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a446b91e73b181f9f4d56264dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)若四棱柱体积为36,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab6ad3d3e3064fa417a02dba02dbf04.png)
您最近一年使用:0次
10 . 如图,已知正方体
的棱长为
,
、
分别为棱
、
的中点.
平面
;
(2)设平面
与平面
的交线为
,求点
到直线
的距离及二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8ec2583c364c079a7b1bfb1e8fe0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad6b3d073d8dd1cb7d9c89116b9d81.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad6b3d073d8dd1cb7d9c89116b9d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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