1 . 如图,在直角梯形
中,
,
,且
,现以
为一边向形外作正方形
,然后沿边
将正方形
翻折,使平面
与平面
互相垂直.
(1)求证:平面
平面
;
(2)求点
到平面
的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/ed66e110-9d08-4051-bf6b-19e3241c7fa6.png?resizew=383)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2 . 如图,在四棱锥
中,底面
是边长为2的正方形,平面
底面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/a7608e76-ef64-48bd-98de-cf273ff97817.png?resizew=148)
(1)证明:平面
平面
;
(2)已知点
是线段
的中点,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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36bd3b2701a86536663fbe6b65a7c61.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/30/a7608e76-ef64-48bd-98de-cf273ff97817.png?resizew=148)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/800faf43a424f2dd708d1426e4e91615.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在四棱锥P﹣ABCD中,PD⊥平面ABCD,底面ABCD是正方形,AC与BD交于点O,E为PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/c950d1fe-cb5f-42e0-80d4-e4ec917957c3.png?resizew=165)
(1)求证:EO
平面PDC;
(2)求证:平面PAC⊥平面PBD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/c950d1fe-cb5f-42e0-80d4-e4ec917957c3.png?resizew=165)
(1)求证:EO
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
(2)求证:平面PAC⊥平面PBD.
您最近一年使用:0次
2023-03-11更新
|
1710次组卷
|
12卷引用:贵州省遵义市道真仡佬族苗族自治县民族高级中学2022-2023学年高二上学期第一次月考数学试题
贵州省遵义市道真仡佬族苗族自治县民族高级中学2022-2023学年高二上学期第一次月考数学试题云南省丽江市2021-2022学年高一下学期期末教学质量监测数学试题辽宁省鞍山市一般高中协作校2022-2023学年高二上学期期初考试数学试题(已下线)第04讲 空间直线、平面的垂直 (高频考点—精讲)-2(已下线)第八章 立体几何初步 讲核心 02江苏省连云港市灌南高级中学2022-2023学年高一下学期第二次月考数学试题2023年2月安徽省普通高中学业水平考试数学模拟试题(二)江西省宜春市丰城市2023届高三上学期1月期末考试数学试题(已下线)第八章 立体几何初步单元测试(基础卷)(已下线)13.2 基本图形位置关系(分层练习)云南省昆明行知中学2022-2023学年高一下学期期末模拟拉练一数学试题(已下线)核心考点08空间直线、平面的垂直-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
名校
解题方法
4 . 如图,在三棱柱
中,侧面
为菱形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/8a5897a8-04d9-41a0-b939-68dc1e69710e.png?resizew=213)
(1)求证:平面
平面
;
(2)已知线段
上存在一点
,使得
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8db421b3e8872ee5add4480da4a291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb24987c2a589ae958def9c7cab5e9d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/8a5897a8-04d9-41a0-b939-68dc1e69710e.png?resizew=213)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)已知线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cabc3303519ac16fc998913ad9f349c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c1e7eafeb3a1695ef9336d44e63394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93316e0e0ed337f62b17408584f14da3.png)
您最近一年使用:0次
名校
解题方法
5 . 已知直三棱柱
中,
,
,点M式
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/1657d64b-6934-4272-90c5-303a76651105.png?resizew=114)
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3419a18ac5c41a3a1ad5369956807cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/1657d64b-6934-4272-90c5-303a76651105.png?resizew=114)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a2712f9cc643d4983d37c9dfe880ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770b4f16694b2bd79a1a93d776a82680.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
您最近一年使用:0次
2022-11-22更新
|
563次组卷
|
6卷引用:贵州省遵义市第一中学2022-2023学年高二上学期第二次月考数学试题
贵州省遵义市第一中学2022-2023学年高二上学期第二次月考数学试题黑龙江省联考2022-2023学年高二上学期期中数学试题辽宁省朝阳市建平县实验中学2022-2023学年高二上学期期中数学试题山东省潍坊市昌乐县昌乐二中2023-2024学年高三上学期9月月考数学试题江苏省盐城市响水中学2022-2023学年高二下学期期中数学试题(已下线)高二下学期期末押题卷01-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修)
名校
解题方法
6 . 如图,在四棱锥
中,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/80212cec-d590-4a47-b533-696441d66afc.png?resizew=190)
(1)证明:平面
平面
;
(2)若平面
平面
,且
,三棱锥
的体积为1,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c630b155517f1788d7b999cab2494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77542024fabe20bd3e4cce840d98cb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/80212cec-d590-4a47-b533-696441d66afc.png?resizew=190)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d7263b36bc05d3ef2082e482c4c479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df5f4a4225ec86ff419be333c3161a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778ba4674ac8501397aea09be7453ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1083037647bea853ab5b73118f27ddd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-10-30更新
|
473次组卷
|
2卷引用:贵州省贵阳第一中学2023届高三上学期高考适应性月考卷(一)数学(文)试题
7 . 如图,在四棱锥
中,底面ABCD是正方形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/7afde5fc-a045-4899-af2c-1df40cdfa3b0.png?resizew=187)
(1)证明:平面
平面
;
(2)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531496172673a735ddf36284fa45fb81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0051d92c8639713847682826c2bb9783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a20de5ab5d40c465b0353fe3c5e589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66536456c67fce11a510d3dad864dc2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/7afde5fc-a045-4899-af2c-1df40cdfa3b0.png?resizew=187)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cc199e2f29f643482f19d8b345ea54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ef387d93efb947fbe046f5f19703e7.png)
您最近一年使用:0次
2022-10-26更新
|
503次组卷
|
4卷引用:贵州省黔东南州凯里市第一中学2023届高三上学期第四次月考数学(文)试题
8 . 如图,在四棱锥
中,
底面ABCD,
,E为棱PD的中点,F是线段PC上一动点.
平面PAB;
(2)若直线BF与平面ABCD所成角的正弦值为
时,求点C到平面AEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb18c7c5391647214d4da31a88202d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12040970d765f83dc194b05fc0a7307d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4787d10940c2bfca1c5aded470034a13.png)
(2)若直线BF与平面ABCD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137f98c6367086cc159aaa5f2e45ee7d.png)
您最近一年使用:0次
2022-10-25更新
|
804次组卷
|
5卷引用:贵州省贵阳市“三新”改革联盟校2022-2023学年高二上学期联考试题(五)数学试题
9 . 在四棱锥
中,已知
底面
,且底面
为矩形,则下列结论中错误的是( )
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016619426725888/3018752047947776/STEM/a8123b9306974bdfa25bf1d327d5eb1a.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016619426725888/3018752047947776/STEM/a8123b9306974bdfa25bf1d327d5eb1a.png?resizew=163)
A.平面![]() ![]() | B.平面![]() ![]() |
C.平面![]() ![]() | D.平面![]() ![]() |
您最近一年使用:0次
10 . 设
,
是两条不同的直线,
,
是两个不同的平面,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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