1 . 如图,在四棱锥
中,
平面
,四边形
是矩形,点
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/2020/12/10/2611395527499776/2613237545279488/STEM/cebca15d-4577-4915-acd0-ad857119c3a9.png)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/dc8d60ee3c8508e0ae2685aece8aa750.png)
![](https://img.xkw.com/dksih/QBM/2020/12/10/2611395527499776/2613237545279488/STEM/cebca15d-4577-4915-acd0-ad857119c3a9.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d682fd0344452998187cb6d48de3dd1.png)
您最近一年使用:0次
2020-12-13更新
|
206次组卷
|
4卷引用:广西桂林市灵川县潭下中学2021-2022学年高二下学期期中考试数学试题
名校
解题方法
2 . 如图,四边形
是正方形,
平面
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b21876717f7a9ba0f0b179ce2aa669c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/49ff9432-c251-46ca-80f8-9e3ddb170c04.png?resizew=182)
(1)求证:
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/39967d6f3aed6ce7b6643787795d451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87e02bff18fba8e9c81de467da297c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b21876717f7a9ba0f0b179ce2aa669c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/49ff9432-c251-46ca-80f8-9e3ddb170c04.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2481914354c3cdb36c1ada923d5b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4718378fec39801c6efa758cb819faa1.png)
您最近一年使用:0次
2020-11-12更新
|
1369次组卷
|
3卷引用:广西南宁三校联考2020-2021学年高二学期高二段考(期中)数学(文)试题
名校
3 . 如图,在直三棱柱
中,
,
,D,E,F分别为AC,
,AB的中点.则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/d097e246-7459-47cc-8703-80e72e0f50d3.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb717228e1762d335814a3adc90eae45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/d097e246-7459-47cc-8703-80e72e0f50d3.png?resizew=165)
A.![]() | B.![]() |
C.EF与![]() ![]() | D.点![]() ![]() |
您最近一年使用:0次
2020-10-12更新
|
2880次组卷
|
18卷引用:广西桂林市第十八中学2022-2023学年高二上学期期中考试数学试题
广西桂林市第十八中学2022-2023学年高二上学期期中考试数学试题广东省中山市第一中学2021-2022学年高二上学期期中数学试题江苏省南京市第十四中学2020-2021学年高二上学期学情调研测试数学试题(已下线)专题8.9 空间向量与立体几何单元测试卷-2021年新高考数学一轮复习学与练江苏省南京师大附中2020-2021学年高二上学期12月阶段检测数学试题江苏省南通中学2020-2021学年高二上学期期末数学试题广东省东莞市东方明珠学校2021届高三下学期5月质量检测数学试题北师大版(2019) 选修第一册 必杀技 第三章 4.3 课时1 用空间向量研究夹角问题重庆市万州第二高级中学2021-2022学年高二上学期第一次月考数学试题苏教版(2019) 选修第二册 限时训练 第10练 空间距离的计算重庆市南华中学校2021-2022学年高二上学期10月月考数学试题2023版 北师大版(2019) 选修第一册 名师精选卷 高考水平模拟性测试(一)河南省郑州市第七中学2022-2023学年高二上学期第一次月考数学试题广东省广州思源学校2022-2023学年高二上学期10月月考数学试题黑龙江省哈尔滨市宾县第二中学2022-2023学年高二上学期第一次月考数学试题北师大版(2019) 选修第一册 数学奇书 学业评价(三十一) 空间中的距离问题重庆市巫溪县尖山中学校2023-2024学年高二上学期第一次月考数学试题内蒙古呼伦贝尔市满洲里远方中学2023-2024学年高二上学期10月月考数学试题
解题方法
4 . 如图所示的几何体中,四边形
是正方形.四边形
是梯形
,
,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/2020/8/18/2530428719104000/2541350020415488/STEM/946dc87c-4dbe-47e2-a00a-a30c37cee63a.png)
(1)求证:
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bce6eba5d07a34f24c5370c580ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db13e8affea90632f591077308119cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3025e649f4d4bc6bbda122f940cf8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c032261d2f887de100ed40e8fc676e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18177e13df82a638280a154aba6e45e.png)
![](https://img.xkw.com/dksih/QBM/2020/8/18/2530428719104000/2541350020415488/STEM/946dc87c-4dbe-47e2-a00a-a30c37cee63a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c0f6b53de48e0f7a09419886276ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ad3801636f311f226766d93859851e.png)
您最近一年使用:0次
2020-09-02更新
|
377次组卷
|
2卷引用:广西柳州市六校2022-2023学年高二上学期期中考试数学试题
名校
5 . 如图,在四棱锥
中,底面
是直角梯形,侧棱
底面
,
垂直于
和
,
,
.
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/66b73252-4509-4f6f-bde5-d40572841747.jpg?resizew=184)
(1)求证:
面
;
(2)求二面角
的正弦值;
![](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/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d11dd7422f4703763abc23d83c7584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/66b73252-4509-4f6f-bde5-d40572841747.jpg?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce25878ca892d27bfc0601c3ce662df0.png)
您最近一年使用:0次
名校
解题方法
6 . 如图所示,四棱锥
中,
平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/4/17/2443664869359616/2445075583254528/STEM/391fb941cff74aa498cc3a46d25a1ee9.png?resizew=183)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405effb49ef901476701e72cc47918da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c6e4f94c57ddbd5fe10a2837e33cbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://img.xkw.com/dksih/QBM/2020/4/17/2443664869359616/2445075583254528/STEM/391fb941cff74aa498cc3a46d25a1ee9.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
您最近一年使用:0次
2020-04-19更新
|
564次组卷
|
4卷引用:广西南宁市第三中学2019-2020学年高二期中段考数学(文)试题
名校
解题方法
7 . 如图,四棱锥
中,
平面
,
,
,
,
分别为线段
,
的中点.
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa6ea683971fa8b6299d7aab6d04092.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011abe509df00fe9410ab08b585ad7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2021-03-28更新
|
170次组卷
|
14卷引用:广西南宁市马山县金伦中学4+N高中联合体2019-2020学年高二上学期期中考试数学试题
广西南宁市马山县金伦中学4+N高中联合体2019-2020学年高二上学期期中考试数学试题四川省乐山四校2017-2018学年高二第三学期半期联考数学(文科)试题安徽省铜陵市第一中学2019-2020学年高二上学期期中数学试题2018年高考数学(文科)二轮复习 精练:大题-每日一题规范练2018-2019学年人教版高中数学选修1-2 模块综合评价(一)黑龙江省海林市朝鲜族中学人教版高中数学选修1-2同步练习:模块终结测评(一)(已下线)实战演练7.2-2018年高考艺考步步高系列数学(已下线)1.6.2 垂直关系的性质(课时作业)-2018版步步高学案导学与随堂笔记数学(北师大版必修2)(已下线)专题23 空间点线面的位置关系-十年(2011-2020)高考真题数学分项辽宁省沈阳市第二中学2019-2020学年度下学期高一年级数学期末考试试题新疆乌鲁木齐市第八中学2018-2019学年高一下学期期末考试数学试题宁夏青铜峡市高级中学2021-2022学年高二上学期第一次月考数学(理)试题山西省运城市稷山中学2023届高三上学期月考(重组五)数学试题(已下线)专题23 立体几何解答题(文科)-1
名校
解题方法
8 . 如图,四边形
为正方形,
平面
,点
分别为
的中点,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/0446923d-d92d-4010-a89c-cb6aec519298.png?resizew=141)
(1)证明:
平面
;
(2)求三棱锥
的体积与三棱锥
的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2682f3f3f0f72c893b99073bcac83ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87261df80b82221732329b6ef3fdda7f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/0446923d-d92d-4010-a89c-cb6aec519298.png?resizew=141)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05479ce59da01ea9c5bef3f20efadb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2020-03-19更新
|
234次组卷
|
2卷引用:南宁市东盟中学2020-2021学年高二年级期中考试数学(文)试题
名校
解题方法
9 . 如图,在四棱柱
中,侧面
底面
,
,底面
为直角梯形,其中
,
,
,O为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/d0700a48-1edf-471a-9e40-ac078e203a28.png?resizew=184)
(1)求证:
平面
;
(2)求凸多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f67c2d29909f744a60448e409f0fbab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d540455054b9781297a1e871949be43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a93f5289c1483bc39b0125fdc8dd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/d0700a48-1edf-471a-9e40-ac078e203a28.png?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6dcab5d5bdeb695b261e21c8491039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
(2)求凸多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b9518b005ce7cccc31b9baed841987.png)
您最近一年使用:0次
2018高三·全国·专题练习
名校
10 . 如图,在矩形
中,
,
为
的中点,现将
与
折起,使得平面
平面
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2020/3/18/2422129589567488/2422980540882944/STEM/5514119e1675449887d5b099be4f0665.png?resizew=392)
(1)求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585288e61871608f6ff8f7e4a0beafbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79798199f1bc7ac85d969ebea1ef6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd3b58d32346a8d31bc90adc67d37b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036a0d3b3c70d41060bc441ddd8003fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7c88c481a78a38809b3abfe64c8d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://img.xkw.com/dksih/QBM/2020/3/18/2422129589567488/2422980540882944/STEM/5514119e1675449887d5b099be4f0665.png?resizew=392)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351d71fa01d3f5920e374a8ee7b524.png)
您最近一年使用:0次
2020-03-19更新
|
231次组卷
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12卷引用:广西南宁市第三中学2021-2022学年高二下学期期中考试数学(理)试题
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