名校
1 . 如图,在五边形
中,四边形
为正方形,
,
,F为AB中点,现将
沿
折起到面
位置,使得
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a6eb75c2bc5a47ec8c8d83d79fd431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db6ff4159947ed2dc47d82fa3bcab9a.png)
A.平面![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.折起过程中,![]() ![]() |
D.三棱锥![]() ![]() |
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2024-06-11更新
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645次组卷
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3卷引用:山东省泰安市2024届高三四轮检测数学试题
2 . 两个向量
和
的叉乘写作
,叉乘运算结果是一个向量,其模为
,方向与这两个向量所在平面垂直.若
,
,则
.如图,已知在四棱锥
中,底面
是直角梯形,
,
,
,
,
,
,
分别是
,
,
,
的中点.
平面
;
(2)已知
,
,
为
中点,以
为原点,
的方向为
轴的正方向建立空间右手直角坐标系.
①求
;
②求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba64ae92194bc4f0f6e49725471542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d32b8e0db81b4ef5184cabb26d05da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c47d736aacb6475407c5a1ddccc0ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e19bfb8bf10f5af770eeb59a375754b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39f704aab45983e7b8af7c2c5c9c9a6.png)
![](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/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0184f9233d2980b84628393246d548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd082397c8b5dd243e4e395c1540960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05479863cf9f41e2ad9f843ea740a3c0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5c40f909fae89547423350cd87398d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a0c299356c26338d4153748e8a61d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5043a1db17715a9a1f1783c755c446ee.png)
②求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8103f08579983694dc41a0af979b94.png)
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名校
3 . 如图,已知四棱台
的上、下底面分别是边长为2和4的正方形,平面
⊥平面ABCD,
,点P是棱
的中点,点Q在棱BC上.
,证明:
平面
;
(2)若二面角
的正弦值为
,求BQ的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253ffd3fc633d861810ee2e872188b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b90595662af9a1936e1e703462cb69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc862687ca2b31b20dd37eb5375cae6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1a378a3a4660eb1ece52085a9b44d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8c5362138fde892955c34074ac5d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4508b5e21a3e74ea980c5b0b691cf689.png)
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2024-03-22更新
|
3536次组卷
|
5卷引用:2024届山东省泰安肥城市高考仿真模拟(二)数学试题
名校
解题方法
4 . 如图,直四棱柱
的底面为平行四边形,
分别为
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
平面
;
(2)若底面
为矩形,
,异面直线
与
所成角的余弦值为
,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814ef3feb3329aab66213f3a6a9d2f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
(2)若底面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc28e69c1ba0aac981256887f7dfa94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a604466a9c8d10d557b3dfc43b547065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105ab9d3410dfa30318f378feb287350.png)
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2024-01-22更新
|
1925次组卷
|
4卷引用:山东省泰安市新泰第一中学老校区(新泰中学)2024届高三上学期高考模拟数学试题
解题方法
5 . 如图1,在平行四边形
中,
,
,
为
的中点,
,
,沿
将
翻折到
的位置,如图2,
.
(1)证明:
平面
;
(2)求平面
和平面
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0760712e3e2ea02b755b751e760d0c55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e0120c0ebacd06d0f93a7f94d46f1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618bb0b9bda4ec0fe03880654a5d3ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ffd9c2bbecf52ab9c1752602856aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593107238588b2bf420045a4d8ef132f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cbf03524f866cc66d019a01e7c4284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca0940f5c21431c089d4f7a221df43c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/6/f99831ee-7398-4904-8dbc-036b588ed717.png?resizew=342)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8167b0685f39f6537d95a95c4de3b38c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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解题方法
6 . 在棱长为
的正方体
中,点
分别是
、
、
的中点,则过线段
且平行于平面
的截面图形的周长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
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解题方法
7 .
为空间中两条不同的直线,
为两个不同的平面,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-06-03更新
|
906次组卷
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2卷引用:山东省泰安肥城市2023届高考适应性训练数学试题(三)
8 . 四棱锥
中,底面
为矩形,
,
,平面
与平面
的交线为
.
(1)求证:直线
平行于平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39564987082f8dfe941c6fa5ba328144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3ff0e6ccd6a6e71fbb175b0ccc71bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/5/3cd72f1f-d419-4140-a3c9-99108561ce6f.png?resizew=130)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bde8b2ab7f5f834aed51a526f1f27a0.png)
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解题方法
9 .
是两个平面,
是两条直线,有下列四个命题其中正确的命题有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
A.如果![]() ![]() |
B.如果![]() ![]() |
C.如果![]() ![]() |
D.如果![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-01-25更新
|
228次组卷
|
36卷引用:2020届山东省泰安市高三模拟考试(一模)数学试题
2020届山东省泰安市高三模拟考试(一模)数学试题2020届山东省泰安市高三一轮检测数学试题山东省菏泽市成武一中2020届高三数学第二次模拟试题山东省济宁市嘉祥县第一中学2019-2020学年高一6月月考数学试题(已下线)【新教材精创】11.4.1直线与平面垂直(第2课时)练习(2)(已下线)专题九 立体几何与空间向量-2020山东模拟题分类汇编山东省实验中学2020-2021学年高三第一次诊断考试(10月)数学试题(已下线)【新东方】杭州新东方高中数学试卷398湖北省鄂州市部分高中联考协作体2020-2021学年高二上学期期中数学试题(已下线)2021届高三数学新高考“8+4+4”小题狂练(13)湖北省恩施州巴东县第二高级中学2020-2021学年高二上学期期中数学试题重庆市三峡名校联盟2020-2021学年高二上学期联考数学试题湖北省随州市第一中学2020-2021学年高三上学期11月月考数学试题云南省昆明市第一中学2021届高三第六次复习检测数学(文)试题云南省昆明市第一中学2021届高三第六次复习检测(2月月考)数学(理)试题(已下线)必刷卷03-2021年高考数学(理)考前信息必刷卷(新课标卷)(已下线)必刷卷03-2021年高考数学(文)考前信息必刷卷(新课标卷)(已下线)2021届高三高考数学适应性测试仿真系列卷四(江苏等八省新高考地区专用)(已下线)2021届高三高考数学适应性测试仿真系列卷一(江苏等八省新高考地区专用)黑龙江省大庆中学2021-2022学年高二上学期开学考试数学试题河北省衡水市五校2021届高三下学期联考(一)数学试题第13章:立体几何初步 - 基本图形及位置关系(B卷提升卷)- 2020-2021学年高一数学必修第二册同步单元AB卷(新教材苏教版)湖北省东南联盟2021-2022学年高二上学期10月联考数学试题(已下线)专题30 空间中直线、平面平行位置关系的证明方法-学会解题之高三数学万能解题模板【2022版】(已下线)专题31 空间中直线、平面垂直位置关系的证明方法-学会解题之高三数学万能解题模板【2022版】江苏省南京市第五中学2021-2022学年高三上学期10月月考数学试题江苏省连云港高级中学2021-2022学年高一下学期第二次阶段测试数学试题重庆市实验中学2021-2022学年高一下学期期末复习(一)数学试题黑龙江省大庆市让胡路区大庆中学2021-2022学年高二上学期数学开学考试试题江苏省泰州中学2022-2023学年高三上学期期初调研考试数学试题(已下线)易错点08 立体几何河南省开封市五校2022-2023学年高一下学期期末联考数学试题广东省罗定中学城东学校2023届高三上学期9月调研数学试题山西省朔州市怀仁市第一中学校、大地学校高中部2023-2024学年高二上学期第一次月考数学试题海南省白沙县海南中学白沙学校2023-2024学年高二上学期期末考试数学试题(已下线)专题04空间点、直线、平面的位置关系与空间直线、平面的平行-期末真题分类汇编(新高考专用)
解题方法
10 . 如图,若
为正六棱台,
,
,
则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/48b64e91-bf2b-4bd3-88ab-4614e021f8e0.png?resizew=254)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858be9a2f30a22cfdebeaa5bf2e45b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188dfa1c5859c7d1084abe8adc559df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/48b64e91-bf2b-4bd3-88ab-4614e021f8e0.png?resizew=254)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.侧棱与底面所成的角为![]() |
您最近一年使用:0次