名校
1 . 在四棱锥
中,E为棱AD的中点,PE⊥平面
,
,
,
,
,F为棱PC的中点.
(1)求证:
平面
;
(2)若二面角
为
,求直线
与平面
所成角的正切值.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ac29b5b40502851b7a24f7ebcc0b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd8e8c759858fb3d3132605d44e865.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/e58d7955-983f-4ce0-908a-2e62e1e81ea2.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea81cfad5da39884e84d257149d7f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-01-14更新
|
533次组卷
|
7卷引用:广东省茂名市第五中学2021-2022学年高二上学期期中数学试题
广东省茂名市第五中学2021-2022学年高二上学期期中数学试题江苏省扬州市高邮市第一中学2021-2022学年高三上学期期中模拟数学试题山西省大同市第一中学校2021-2022学年高二上学期10月月考数学试题新疆喀什地区岳普湖县2022届高三第一次模拟考试数学(文)试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-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)山东省济宁市第一中学2024届高三上学期期末数学试题
名校
2 . 将正方形ABCD沿对角线BD折成直二面角
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
A.![]() ![]() | B.![]() |
C.AB与平面BCD所成的角为60° | D.AB与CD所成的角为90° |
您最近一年使用:0次
2022-11-19更新
|
555次组卷
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4卷引用:广东省深圳外国语学校2021-2022学年高二上学期期中数学试题
广东省深圳外国语学校2021-2022学年高二上学期期中数学试题辽宁省鞍山市2022-2023学年高二上学期期中数学试题(已下线)6.3.3空间角的计算(2)(已下线)第一章 空间向量与立体几何单元测试(基础版)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
名校
3 . 如图,在四棱锥
中,底面
是边长为2的菱形,
,平面
平面
,点
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888496258179072/2889214410711040/STEM/65f3016d63754590863fcbfc5f8bdf55.png?resizew=118)
(1)求证:
;
(2)若
与平面
所成角为
,求二面角
的余弦值.
![](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/8469f2a84fbce3195e31ddd413e5f8ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b77a5c3865855fbb3d24f9522ced8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888496258179072/2889214410711040/STEM/65f3016d63754590863fcbfc5f8bdf55.png?resizew=118)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd7c2767c106faf27d6a97ebc8e739.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d733daf111889f16d5404b731d40fd12.png)
您最近一年使用:0次
解题方法
4 . 如图,平面五边形
中,
是边长为2的等边三角形,
,
,
,将
沿
翻折成四棱锥
,
是棱
上的动点(端点除外),
、
分别是
、
的中点,且___________.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/77386a20-3dc7-4f81-8183-e0061835a65d.png?resizew=276)
请从下面三个条件中任选一个,补充在上面的横线上,并作答:
①
;②
;③点
在平面
的射影在直线
上.
(1)求证:
;
(2)当
与平面
所成角最大时,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1e3a43d0fa18f6c0888ba804d5b329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8057cf3b7c9c34fbf92391e2b742f0b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/77386a20-3dc7-4f81-8183-e0061835a65d.png?resizew=276)
请从下面三个条件中任选一个,补充在上面的横线上,并作答:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b5169b1d6082c2e148e37202c57d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f82a30d6b232dc4d8f35d2d6e0e0f42.png)
![](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/03902478df1a55bc99703210bccab910.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e831b14af240276a6d4ce63b132488.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2021-11-26更新
|
379次组卷
|
3卷引用:广东省深圳实验学校光明部2021-2022学年高二上学期期中数学试题
广东省深圳实验学校光明部2021-2022学年高二上学期期中数学试题第三章空间向量与立体几何 章末测评卷-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)模块二 专题1《空间向量与立体几何》单元检测篇 B提高卷(人教A)
5 . 在棱长为1的正方体
中,已知
为线段
的中点,点
和点
分别满足
,
,其中
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0971e9acef6d8d6553cdae7f9cd1569e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af7c4efac77a963ec845b7ef25cc7747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() |
B.当![]() ![]() ![]() |
C.若直线![]() ![]() ![]() ![]() |
D.存在唯一的实数对![]() ![]() ![]() |
您最近一年使用:0次
2021-11-26更新
|
369次组卷
|
3卷引用:广东省深圳实验学校光明部2021-2022学年高二上学期期中数学试题
名校
6 . 在棱长为1的正方体
中,点P满足
,
,
,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f102d05748b5cdec85905b097264c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
您最近一年使用:0次
2021-11-23更新
|
708次组卷
|
20卷引用:广东省广州市仲元中学2021-2022学年高二上学期期中数学试题
广东省广州市仲元中学2021-2022学年高二上学期期中数学试题江苏省南通市海安高级中学2021-2022学年高三上学期期中模拟数学试题重庆市万州第二高级中学2021-2022学年高二上学期期中数学试题山东省青岛市4区市2021-2022学年高二上学期期中考试数学试题重庆市第七中学校2021-2022学年高二上学期期中数学试题福建省南平市浦城县2021-2022学年高二上学期期中考试数学试题福建省厦门第一中学2021-2022学年高二上学期期中考试数学试题湖北省恩施州2021-2022学年高三上学期第一次教学质量监测数学试题湖北省宜昌市夷陵中学2021-2022学年高二上学期10月阶段性检测数学试题重庆市杨家坪中学2021-2022学年高二上学期第二次月考数学试题 (已下线)第33讲 立体几何中的范围与最值问题-2022年新高考数学二轮专题突破精练(已下线)考点35 立体几何中的综合问题-备战2022年高考数学典型试题解读与变式(已下线)专题35 立体几何中的探索性问题求解策略-学会解题之高三数学万能解题模板【2022版】辽宁省大连市金普新区省示范性高中联合体2021-2022学年高三第四阶段考试(下学期开学考试)数学试题(已下线)专题06 空间向量与立体几何(突破训练)-备战2022年高考数学二轮复习重难考点专项突破训练(全国通用)山东省枣庄市薛城区2021-2022学年高二上学期期末数学试题(已下线)专题23 立体几何中的压轴小题-2安徽省六安市舒城中学2022-2023学年高二上学期第二次月考数学试题福建省永安市第九中学2022-2023学年高二上学期9月月考数学试题辽宁省辽河油田第二高级中学2022-2023学年高三上学期期末考试数学试题
解题方法
7 . 如图,设E,F分别是正方体
的棱DC上两点,且
,
,其中正确的命题为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/9fc45b37-cebd-43cb-948e-bc4de218ee3a.png?resizew=220)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/9fc45b37-cebd-43cb-948e-bc4de218ee3a.png?resizew=220)
A.三棱锥![]() |
B.异面直线![]() ![]() |
C.直线![]() ![]() |
D.二面角![]() |
您最近一年使用:0次
8 . 如图,已知多面体
,
,
,
均垂直于平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852651028824064/2853489071775744/STEM/543f264c28d24d788a943f4c888d95e5.png?resizew=271)
(1)证明:
平面
;
(2)求直线
与平面
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d17d14819681c455a91d7678742368.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1be17e0a3e51cde1f50f384198e71e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc07af94c2ebedcab772b2b90ff1332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede14ef03dc3666b8a6902ddaf0021b6.png)
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852651028824064/2853489071775744/STEM/543f264c28d24d788a943f4c888d95e5.png?resizew=271)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2e84d6e368f8368f8301c4cd66d6dd.png)
您最近一年使用:0次
20-21高一·全国·课后作业
名校
解题方法
9 . 在长方体
中,
,
,
与平面
所成的角为
,则直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295aced98768ce261e00fe6660a427a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-10-19更新
|
473次组卷
|
3卷引用:广东省揭阳市普宁市华侨中学2021-2022学年高二上学期期中数学试题
广东省揭阳市普宁市华侨中学2021-2022学年高二上学期期中数学试题广东省华中师范大学海丰附属学2021-2022学年高二上学期期中数学试题(已下线)专题13.2 本图形位置关系(重点练)-2020-2021学年高一数学十分钟同步课堂专练(苏教版2019必修第二册)
10 . 如图,正方体
的棱长为1,E为
的中点.F为
的中点,则( )
![](https://img.xkw.com/dksih/QBM/2021/10/16/2830448772562944/2830578772869120/STEM/f54deb08-c51b-4991-8d29-8c4d0cae7153.png?resizew=232)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
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A.![]() | B.直线![]() ![]() |
C.直线EF与平面![]() ![]() | D.点B到平面![]() ![]() |
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2021-10-18更新
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452次组卷
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3卷引用:广东省佛山市顺德区华侨中学2021-2022学年高二上学期期中数学试题