解题方法
1 . 如图,在正方体
中,E是棱
上的动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/9e0f988b-a205-4fe0-b147-f46c6c4e3211.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/9e0f988b-a205-4fe0-b147-f46c6c4e3211.png?resizew=160)
A.直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.二面角![]() |
D.直线![]() ![]() |
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2 . 如图,在直三棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/77ad79b6-0906-4c6a-a511-0af51f8c90bc.png?resizew=142)
(1)证明:直线
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae1b5a1a3f5cb44a771944e1534563b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/8/77ad79b6-0906-4c6a-a511-0af51f8c90bc.png?resizew=142)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7994f25559402687fa7f7d8a3966928.png)
您最近一年使用:0次
名校
3 . 如图,四棱锥
中,
平面
,过
的平面分别与棱
交于点M,N.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/e95dc946-c25c-4d15-a1b0-4b07fc31b4e8.png?resizew=155)
(1)求证:
;
(2)记二面角
的大小为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a632c970535e3dc49bb46519275882e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82fd2c740aea7423ecc2077ed899260.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/e95dc946-c25c-4d15-a1b0-4b07fc31b4e8.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a87e85906b2ee9c5d88d271b748ec33.png)
(2)记二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e13c1dc9dee7eb7aed3d3ef41b2123a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
您最近一年使用:0次
2024-01-17更新
|
489次组卷
|
3卷引用:北京市海淀区2023-2024学年高二上学期期末练习数学试卷
名校
解题方法
4 . 如图,在正方体
中,直线
与直线
所成角的大小为___ ;平面
与平面
夹角的余弦值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
您最近一年使用:0次
2024-01-17更新
|
401次组卷
|
4卷引用:北京市房山区2023-2024学年高二上学期期末考试数学试卷
北京市房山区2023-2024学年高二上学期期末考试数学试卷北京市门头沟区大峪中学2023-2024学年高二下学期开学考试数学试题(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)(已下线)专题04 空间点﹑直线﹑平面之间的位置关系-《知识解读·题型专练》(人教A版2019必修第二册)
解题方法
5 . 正方体
中,
是
的中点,
是线段
上的一点.给出下列命题:
①平面
中一定存在直线与平面
垂直
②平面
中一定存在直线与平面
平行
③平面
与平面
所成的锐二面角不小于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④当点
从点
移动到点
时,点
到平面
的距离逐渐增大
其中正确命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/0cc80a7f-880f-4ba7-827b-b86d3243bff5.png?resizew=159)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
②平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
③平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
其中正确命题的序号是( )
A.②③ | B.①③ | C.①④ | D.②④ |
您最近一年使用:0次
6 . 如图,在四棱锥
中,底面
是边长为1的正方形,
是等边三角形,
为
的中点,且
底面
,点
为棱
上一点.给出下面四个结论:
,都有
;
②存在点
,使
平面
;
③二面角
的正切值为
;
④平面
平面
.
其中所有正确结论的序号是____________ .
![](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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7998a289f6d03dd2a12a3196e5b870d2.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c442d76d4e905000104346d0bb4c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
③二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
④平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
7 . 以等腰直角三角形
的斜边
上的高
为折痕,把
和
折成互相垂直的两个平面后,某学生得出下列四个结论:
①
:
②
是等边三角形;
③三棱锥
是正三棱锥;
④平面
平面
.
其中正确的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/4c101bd5-f125-4678-b973-8f78fd421f6b.png?resizew=334)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
④平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351464da41a2bd5d431d9c427382f1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
其中正确的个数是( )
A.1个 | B.3个 | C.2个 | D.4个 |
您最近一年使用:0次
8 . 如图,四棱锥
中,底面是边长为2的正方形,
是等边三角形,平面
平面
,
,
,
分别为棱
,
,
的中点,
为
及其内部的动点,满足
平面
,给出下列四个结论:
①直线
与平面
所成角为
;
②二面角
的余弦值为
;
③点
到平面
的距离为定值;
④线段
长度的取值范围是
.__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c009f663ad2b0c3ba521daf4b86b066f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c009f663ad2b0c3ba521daf4b86b066f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a6bbce864436c0954a03440531f598.png)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
②二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1ae4a2a697ce14f87af49d2a75e747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
③点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a6bbce864436c0954a03440531f598.png)
④线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b587e5f500e7fb3f4482cc8250255a.png)
您最近一年使用:0次
名校
9 . 如图,在正方体
中,下列结论错误 的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.直线![]() ![]() |
D.平面![]() ![]() ![]() |
您最近一年使用:0次
2023-09-08更新
|
505次组卷
|
5卷引用:北京市日坛中学2023-2024学年高二上学期10月月考数学试题
北京市日坛中学2023-2024学年高二上学期10月月考数学试题(已下线)第10章 空间直线与平面(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)山东省青岛市莱西市2022-2023学年高一下学期期中数学试题(已下线)模块五 高一下期中重组篇(山东)广东省东莞市海逸外国语学校2023-2024学年高一下学期第三次质量检测数学试题
名校
解题方法
10 . 如图,在三棱锥
中,
和
均为正三角形,
,二面角
的大小为
,则异面直线
与
所成角的余弦值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-07-13更新
|
1086次组卷
|
6卷引用:北京市第九中学2023-2024学年中高二下学期开学考试数学试题
北京市第九中学2023-2024学年中高二下学期开学考试数学试题四川省资阳市乐至中学2023-2024学年高二上学期开学考试数学试题四川省绵阳市2022-2023学年高一下学期期末数学试题(已下线)模块二 专题4 立体几何中的平行与垂直的位置关系 基础卷A(已下线)模块二 专题7 立体几何中的平行与垂直的位置关系 基础卷A(已下线)专题8.7 空间直线、平面的垂直(二)【八大题型】-举一反三系列