名校
解题方法
1 . 在四棱锥
中,平面
⊥平面
,底面
为梯形,
,
,且
,
,
.
(1)求证:
;
(2)求二面角______的余弦值;
从①
,②
,③
这三个条件中任选一个,补充在上面问题中并作答.
(3)若
是棱
的中点,求证:对于棱
上任意一点
,
与
都不平行.
![](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/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e04d8312c0ef5305ebfd7b4e71b317f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88197da08544c0dd0f8fb1359797ac9b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
(2)求二面角______的余弦值;
从①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715cc9ea5e7d80930284ffb117142770.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
您最近一年使用:0次
2022-06-19更新
|
633次组卷
|
11卷引用:专练8 专题强化练2-空间向量与立体几何的综合应用-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)
(已下线)专练8 专题强化练2-空间向量与立体几何的综合应用-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)(已下线)期中考试重难点专题强化训练(1)——向量的综合运用-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)2020届北京市朝阳区六校联考高三年级四月份测试数学试题A苏教版(2019) 必修第二册 过关斩将 第13章 13.2 综合拔高练2023版 湘教版(2019) 必修第二册 过关斩将 第4章 综合拔高练(已下线)模块三 专题9(劣构题)拔高能力练(北师大版)四川省宜宾市叙州区第二中学校2022-2023学年高一下学期期末数学试题(已下线)模块三 专题9(劣构题)拔高能力练(人教B)(已下线)模块三 专题9(劣构题)拔高能力练人教A版)江苏省连云港高级中学2021-2022学年高一下学期期末模拟数学试题(已下线)模块三 专题10(劣构题)拔高能力练(苏教版)
名校
2 . 已知三棱锥
中,
.
(1)求证:平面
平面
;
(2)求二面角
的余弦值;
(3)若点M在线段
上,满足
,点N在线段
上,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181f49f169aa408109fbafdab077a891.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
(3)若点M在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7cf1b9fa4914fe152dccc7da221b0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79498e1df1280868532f59ee8059a223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3dbfc9719c6646d58bda36dba623902.png)
您最近一年使用:0次
解题方法
3 . 如图所示,在矩形
中,
,
,
为
的中点,沿
将△
翻折,使二面角
为直二面角.
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879458204426240/2880095439290368/STEM/7748ca21-eb0b-481c-a3cb-d5f4de119ac5.png?resizew=431)
(1)求证:
;
(2)求
与平面
所成角的大小;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd9f345915ae742ed3dcd3f9678264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b32570d553161be04d13954e92a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18a490a22cac27417ddc794f00a1941.png)
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879458204426240/2880095439290368/STEM/7748ca21-eb0b-481c-a3cb-d5f4de119ac5.png?resizew=431)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151e948feebdf7b91fbe739feafa9bc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164e1cc74e41a2a55d3767c006392bfd.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db1d8f228c87b65a3609f825fc441d5.png)
您最近一年使用:0次
2021-12-25更新
|
700次组卷
|
2卷引用:人教A版(2019) 选修第一册 实战演练 第一章 易错疑难突破专练
名校
解题方法
4 . 如图1,在矩形ABCD中,AB=1,BC=2,点E为AD的中点,将△ABE沿直线BE折起至平面PBE⊥平面BCDE(如图2),点M在线段PD上,
平面CEM.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/29/9a22444f-c561-4f39-8192-02a002cd461b.png?resizew=395)
(1)求证:MP=2DM;
(2)求二面角B-PE-C的大小;
(3)若在棱PB、PE上分别取中点F、G,试判断点M与平面CFG的关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752206b0d1c5dddf6840fb6b8252240.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/29/9a22444f-c561-4f39-8192-02a002cd461b.png?resizew=395)
(1)求证:MP=2DM;
(2)求二面角B-PE-C的大小;
(3)若在棱PB、PE上分别取中点F、G,试判断点M与平面CFG的关系,并说明理由.
您最近一年使用:0次
2022-04-23更新
|
406次组卷
|
4卷引用:北京市海淀区教师进修学校附属实验学校2020-2021学年高二上学期期中数学试题
名校
解题方法
5 . 在二面角的棱上有两个点
、
,线段
、
分别在这个二面角的两个面内,并且都垂直于棱
,若
,
,
,
,则这个二面角的大小为( )
![](https://img.xkw.com/dksih/QBM/2021/12/4/2848404014669824/2870450356092928/STEM/787984ea0783461fb7d1a3cf8dd519a6.png?resizew=268)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321f96c4f808afe67cf565ca74ae0351.png)
![](https://img.xkw.com/dksih/QBM/2021/12/4/2848404014669824/2870450356092928/STEM/787984ea0783461fb7d1a3cf8dd519a6.png?resizew=268)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-12-11更新
|
1747次组卷
|
11卷引用:浙江省杭州市八校联盟2021-2022学年高二上学期期中联考数学试题
浙江省杭州市八校联盟2021-2022学年高二上学期期中联考数学试题山西省运城市2021-2022学年高二上学期期末数学试题广东省东莞实验中学2022-2023学年高二上学期月考一数学试题(已下线)1.2.4 二面角(分层训练)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第一册)广东省东莞市厚街中学2023-2024学年高二上学期第一次月考数学试题广东省肇庆中学2021-2022学年高二上学期学段考试(三)数学试题(已下线)解密15 空间向量与立体几何 (分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)浙江省宁波市余姚中学2022-2023学年高二上学期10月月考数学试题(已下线)6.3.3 空间角的计算(练习)-2022-2023学年高二数学同步精品课堂(苏教版2019选择性必修第二册)(已下线)第33讲二面角的几何求法广东省佛山市顺德区罗定邦中学2023-2024学年高二上学期期中数学试题
名校
解题方法
6 . 在直三棱柱
中,
,二面角
的大小为
,点
到平面
的距离为
,点
到平面
的距离为
,则异面直线
与
所成角的余弦值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1654dfe63f11563eadbaee32dae7b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知三棱柱
,平面
平面
,
,
,
是边长为2的等边三角形.
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854019742351360/2855252281868288/STEM/c03aa44f-3830-4ba6-b33e-a23927529a70.png?resizew=216)
(1)求二面角
的大小的正切值;
(2)求直线
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4020513c097ba34df4b42e297f892cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9e70f2d6097dd263f3eb66e2256fd1.png)
![](https://img.xkw.com/dksih/QBM/2021/11/18/2854019742351360/2855252281868288/STEM/c03aa44f-3830-4ba6-b33e-a23927529a70.png?resizew=216)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185729402f3b20ac3e0b003be9b385eb.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
名校
解题方法
8 . 在正三角形ABC中,E、F、P分别是AB、AC、BC边上的点,满足
(如图1).将
沿EF折起到
的位置,使二面角
成直二面角,连接A1B、A1P(如图2)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/b548b964-04cc-4f37-a113-79a18b165ac8.png?resizew=398)
(1)求证:
平面BEP;
(2)求直线A1E与平面A1BP所成角的大小;
(3)求二面角B﹣A1P﹣F的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06ee44206d4e110610bc412f11f2ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2d555062f34d5a74f6d47da4ea8888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc14ed237a4bcc35cbd1f5f1321b3718.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/b548b964-04cc-4f37-a113-79a18b165ac8.png?resizew=398)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4525c00ed908bed8ba8d353e747a858.png)
(2)求直线A1E与平面A1BP所成角的大小;
(3)求二面角B﹣A1P﹣F的余弦值.
您最近一年使用:0次
2021-11-15更新
|
429次组卷
|
4卷引用:上海市交通大学附属中学闵行分校2021-2022学年高二上学期10月月考数学试题
上海市交通大学附属中学闵行分校2021-2022学年高二上学期10月月考数学试题上海市徐汇区南洋模范中学2021-2022学年高二上学期期中数学试题(已下线)上海高二上学期期中【常考60题考点专练】(2)(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
解题方法
9 . 如图,已知
平面
,
,
,
,PB=
,则二面角
的大小为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0653ca05309f7e7529e1f16a68d17fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b23baad577f54189810194d955461a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6119c2903ab5fb1509fcb17b5f53cb0c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/9acd16aa-8e7a-4d34-887c-097dd476477c.png?resizew=143)
您最近一年使用:0次
2021-10-29更新
|
357次组卷
|
4卷引用:上海市奉贤区致远高级中学2021-2022学年高二上学期10月评估数学试题
名校
10 . 如图,已知
、
分别是正方形
边
、
的中点,
与
交于点
,
、
都垂直于平面
,且
,
,
是线段
上一动点.
![](https://img.xkw.com/dksih/QBM/2021/10/15/2830072873754624/2831822349582336/STEM/a1c685e9-e713-4edd-9337-368441bd36b9.png?resizew=285)
(1)求证:
平面
;
(2)若
平面
,试求
的值;
(3)当
是
中点时,求二面角
的余弦值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18091448701460b53e076331e7c575cc.png)
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(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad337a2ee42c1d43458859014c54b92.png)
(3)当
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da17111d46f81cb18e994291fe0786f.png)
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