名校
解题方法
1 . 如图,在三棱锥
中,
、
、
分别为
、
、
的中点,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/3cb8b0ec-4f3b-47cd-850b-0591955dd406.png?resizew=166)
(1)求证:平面
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b7675ff57bdccb95a8241c1cd09f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb72aef223aa918128040bd63233144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183dc8b0b923fe55b537be5724853901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bc7774144c164f7ebaeca54fa657e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/3cb8b0ec-4f3b-47cd-850b-0591955dd406.png?resizew=166)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392e71a9d1ebe4577f785581d0142305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0f9bc9123d19a09babe8609cf12327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
您最近一年使用:0次
2021-02-08更新
|
457次组卷
|
2卷引用:海南省三亚华侨学校2020-2021学年高二下学期返校考试数学试题
名校
2 . 如图所示,在四棱锥E-ABCD中,底面ABCD是菱形,∠ADC=60°,AC与BD交于点O,EC⊥底面ABCD,F为BE的中点,AB=CE.
![](https://img.xkw.com/dksih/QBM/2021/8/1/2777023834357760/2821658110623744/STEM/b2d9f0d6053e44ac85d45db35db4ecb1.png?resizew=145)
(1)求证:DE∥平面ACF;
(2)求异面直线EO与AF所成角的余弦值;
(3)求AF与平面EBD所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2021/8/1/2777023834357760/2821658110623744/STEM/b2d9f0d6053e44ac85d45db35db4ecb1.png?resizew=145)
(1)求证:DE∥平面ACF;
(2)求异面直线EO与AF所成角的余弦值;
(3)求AF与平面EBD所成角的正弦值.
您最近一年使用:0次
2021-10-03更新
|
525次组卷
|
10卷引用:海南省海口市第一中学2019-2020学年高三上学期10月月考数学试题
海南省海口市第一中学2019-2020学年高三上学期10月月考数学试题2020届海南省儋州市第一中学高三上学期第二次月考数学试题【校级联考】2019年 塘沽一中、育华中学高三毕业班第三次模拟考试数学(文史类)人教A版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 专题强化练1 利用空间向量基本定理解决立体几何问题(已下线)专题01 空间向量与立体几何-利用空间向量基本定理解决立体几何问题-2021-2022学年高二数学同步练习和分类专题教案(人教A版2019选择性必修第一册)(已下线)专题03 空间向量与立体几何的压轴题(一)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)(已下线)专题1.3 空间向量与立体几何 章末检测3(难)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(人教A版2019选择性必修第一册)(已下线)1.2空间向量基本定理C卷广东省广州市九十七中2023-2024学年高二上学期第一次月考数学试题(已下线)上海市徐汇中学2023-2024学年高三上学期期中考试数学试题变式题16-21
2014高三·全国·专题练习
名校
解题方法
3 . 如图,在四棱锥
中,底面
是边长为
的正方形,侧面
底面
,且
,若
、
分别为
、
的中点,求证:
![](https://img.xkw.com/dksih/QBM/2022/3/28/2945825533640704/3000684830597120/STEM/885421cd9f364e55b187dfeb967bfa3e.png?resizew=209)
(1)
侧面
;
(2)
平面
.
![](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/0a6936d370d6a238a608ca56f87198de.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/c1b7201f9eb7e7c10042c096e0c9f15c.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2945825533640704/3000684830597120/STEM/885421cd9f364e55b187dfeb967bfa3e.png?resizew=209)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
您最近一年使用:0次
2022-06-13更新
|
944次组卷
|
9卷引用:海南省海南枫叶国际学校2019-2020学年高二上学期期中数学试题
海南省海南枫叶国际学校2019-2020学年高二上学期期中数学试题(已下线)2014届高考数学总复习考点引领+技巧点拨第八章第3课时练习卷2017届江苏苏州市高三暑假自主学习测试数学试卷云南省南涧彝族自治县民族中学2017-2018学年高二9月月考数学(文)试题甘肃省武威第十八中学2017-2018学年高二下学期第二次月考数学(文)试题甘肃省武威第十八中学2018-2019学年高一上学期期末考试数学试题河南省扶沟县第二高级中学2021-2022学年高一上学期第二次考试数学试题云南省昆明市官渡区第一中学2021--2022学年高一6月月考数学试题福建省将乐县第一中学2022-2023学年高一下学期第三次月考数学试题
名校
解题方法
4 . 如图,在四棱锥
中,
平面
,
∥
,
,
,
分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/93609158-a543-4e16-a1e5-f81b3d3c917b.png?resizew=225)
(1)求证:
∥平面
.
(2)求证:平面
⊥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3089285ebb92a2cf4f4e52ad59e173.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/a16dd8f6cb6a8aadd39ca731febe0ae2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/93609158-a543-4e16-a1e5-f81b3d3c917b.png?resizew=225)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212a67f115d1cbe69f100b489babe5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2021-12-24更新
|
409次组卷
|
4卷引用:海南省海口市海港学校2022届高三上学期第四次考试数学试题
19-20高一·浙江杭州·期末
名校
解题方法
5 . 如图,在四面体
中,
平面
,
,
,
.M是
的中点,P是
的中点,点Q在线段
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/13/ae741a5c-e8ac-4faf-9881-9767d93b3cdb.png?resizew=202)
(1)证明:
平面
;
(2)若二面角
的大小为
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/13/ae741a5c-e8ac-4faf-9881-9767d93b3cdb.png?resizew=202)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b70049601f57c8a2ece170c0a9c3c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a72dfbf0138a611174c36ce077e0c47.png)
您最近一年使用:0次
2020-11-09更新
|
187次组卷
|
4卷引用:海南省海口中学2022届高三上学期第二次月考数学试题
名校
6 . 四棱锥
,底面
为平行四边形,侧面
底面
.已知
,
,
,
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/1bbb4e4a-bc55-41fc-ab32-0b2590aa2626.png?resizew=148)
(1)求证:
平面
;
(2)求平面
与平面
所成二面角的余弦值.
![](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/5b6e6192cf24ada791c26c2d6d434069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6c7dde86da81fd9dade00635397c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ac2e11788860424508ea9e80cf89d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f407f0d2e4448b9249a466bc0d95f188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/1bbb4e4a-bc55-41fc-ab32-0b2590aa2626.png?resizew=148)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d50356a01ae13936f1bd8efa94c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f177b07e6042b34bc2666db725a9d68a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
您最近一年使用:0次
名校
7 . 棱锥
中,底面
是矩形,
底面
,
是
的中点,已知
,
,
,求:
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571494194323456/2571859572441088/STEM/a02f0bb3374f47a3a0cd0eb94b77a3a0.png?resizew=187)
(1)求证:PA//平面BED;
(2)求异面直线
与
所成的角的大小.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c3ec174b1ce835cc8737ff6ce57e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571494194323456/2571859572441088/STEM/a02f0bb3374f47a3a0cd0eb94b77a3a0.png?resizew=187)
(1)求证:PA//平面BED;
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
名校
8 . 如图,已知四棱锥
中,底面
为菱形,
,
平面
,
,E,F分别为BC,PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/463edb66-a15c-44ee-bab2-ee37e562da04.png?resizew=139)
(1)求证:PB∥平面AFC;
(2)求平面PAE与平面PCD所成锐二面角的余弦值.
![](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/e075468e7fb0bf30229aec01a7205977.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/96127e45e2dd2494fccb1c0905951f0b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/463edb66-a15c-44ee-bab2-ee37e562da04.png?resizew=139)
(1)求证:PB∥平面AFC;
(2)求平面PAE与平面PCD所成锐二面角的余弦值.
您最近一年使用:0次
20-21高一上·全国·课后作业
名校
解题方法
9 . 如图,四棱锥P﹣ABCD的底面ABCD为菱形,PB=PD,E,F分别为AB和PD的中点.
(2)求证:平面PBD⊥平面PAC.
(2)求证:平面PBD⊥平面PAC.
您最近一年使用:0次
2020-09-23更新
|
4858次组卷
|
15卷引用:海南省琼海市嘉积中学2021-2022学年高一下学期期末数学试题
海南省琼海市嘉积中学2021-2022学年高一下学期期末数学试题(已下线)第08章+立体几何初步(A卷基础篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版)(已下线)第八章知识总结及测试-2020-2021学年高一数学一隅三反系列(人教A版2019必修第二册)广东省雷州市第二中学2020-2021学年高二上学期期中数学试题黑龙江省大庆市第二中学2020-2021学年高一下学期期末数学试题陕西省安康中学,安康中学分校,高新中学等2021-2022学年高二上学期期中联考文科数学试题湖南省郴州市2021-2022学年高一下学期期末数学试题湖南省长沙市宁乡市2021-2022学年高二下学期期末数学试题天津市南开区2022-2023学年高一下学期6月阶段性质量检测(期末)数学试题山西省阳高县第一中学校2022-2023学年高一下学期期末数学试题内蒙古巴彦淖尔市临河区第三中学2021-2022学年高三(计算机班)上学期期末数学试题专题05 空间直线、平面的垂直-《期末真题分类汇编》(新高考专用)陕西省宝鸡市扶风县法门高中2023-2024学年高一下学期期中考试数学试卷宁夏回族自治区石嘴山市第三中学2023-2024学年高一下学期5月月考数学试题(已下线)专题04 空间中的平行、垂直关系-期末真题分类汇编(天津专用)
解题方法
10 . 如图所示,在三棱柱
中,
,且
平面
,点
是
上的一点,求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/4d005d6b-7253-425b-b995-d06d8640bdff.png?resizew=123)
(I)
平面
;
(II)平面
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fe926770d2354e172dec02f5ce2efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/4d005d6b-7253-425b-b995-d06d8640bdff.png?resizew=123)
(I)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68fdb2b9d6a4a54ed1328c5b3adcf7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(II)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c5088536dad890222fe47df3de5efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b94e97d085cea077cb82a0b7d2f523e.png)
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