1 . 如图
为直三棱柱,
,
,设
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/614f9a67-f2f0-493a-8c27-de4544365149.png?resizew=152)
(1)证明
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46720eabe78e309e02c24678632b586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/614f9a67-f2f0-493a-8c27-de4544365149.png?resizew=152)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8a2f9862ddd955ab46721ff764f2ec.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
您最近一年使用:0次
2024-01-25更新
|
109次组卷
|
2卷引用:四川省凉山州2023-2024学年高二上学期期末检测数学试卷
2 . 如图,在四棱锥
中,
底面ABCD,底面ABCD是直角梯形,
,
,
,
,E点在AD上,且
.
(1)求证:平面
平面PAC;
(2)若直线PC与平面PAB所成的角为45°,求二面角
的余弦值.
![](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/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6060d9a82ed5405a1ea8cd824448b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ab1959f7fa560977ffb9fb0e11bb2c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/6/1def66f2-a161-4d82-a613-6427d184c11d.png?resizew=149)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
(2)若直线PC与平面PAB所成的角为45°,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8981acad5791c9037b86779e4d8323.png)
您最近一年使用:0次
2023-11-14更新
|
1255次组卷
|
7卷引用:四川省凉山州西昌市2023-2024学年高二上学期期末考试数学试题
四川省凉山州西昌市2023-2024学年高二上学期期末考试数学试题重庆市部分区2022-2023学年高二上学期期末联考数学试题(已下线)模块一 专题2 利用空间向量解决立体几何问题 (讲)2 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)高二上学期期末数学模拟试卷(人教A版2019选择性必修第一册+第二册)-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019)(已下线)第02讲:空间向量与立体几何交汇(必刷6大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019选择性必修第一册)新疆维吾尔自治区昌吉市第一中学2023-2024学年高二上学期12月月考数学试题四川省眉山市仁寿第一中学校南校区2024届高三上学期12月月考数学(理)试题
名校
3 . 如图,在四棱锥
中,
,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/e3aafac1-6f9c-4327-87ef-794afc4414d5.png?resizew=176)
(1)求证:
面
;
(2)点
在棱
上,设
,若二面角
余弦值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044023bf62e87cb9002ba2974f74bc49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc10330e0827026b78343a4f0ead282f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29c9bf1a6582c093b30e429f3b6ca9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/e3aafac1-6f9c-4327-87ef-794afc4414d5.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34cf4760da098099493d4627dacb878.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a7d6e106dbdb0ae79f77462faf768a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deffc349cbe3464f41c7965d32ef53b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-10-27更新
|
2034次组卷
|
7卷引用:四川省凉山州宁南中学2023-2024学年高二上学期期末模拟数学试题(二)
4 . 在四棱锥
中,
底面
,
为等腰梯形,
,
,
.
(1)求证
;
(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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e328ff490d0ca18aa10445c3586c185.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/343b1ab5-bd54-43ce-a8db-df8d478b7f50.png?resizew=182)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
名校
5 . 如图,四棱锥
的底面
是菱形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/2ef2ae64-cd25-49be-9072-599f43489362.png?resizew=181)
(1)求证:
平面PBD;
(2)若E为
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/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ff87102c14ae8c4c99c825ecf7d9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/2ef2ae64-cd25-49be-9072-599f43489362.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
(2)若E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,四棱锥
的底面ABCD是菱形,
,
,
,E为PD的中点.
(1)求证:
平面ACE;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ff87102c14ae8c4c99c825ecf7d9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/30/3ca2153f-8268-4add-9dd3-a8f6e41947ea.png?resizew=167)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
您最近一年使用:0次
名校
7 . 已知在多面体
中,
,
,
,
,
且平面
平面
.
(1)设点F为线段BC的中点,试证明
平面
;
(2)若直线BE与平面ABC所成的角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066cd386723885c535ea720f5817847a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0028211551dd418eaaf51dde450f8b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5545dc3211671941048034af38092fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236c134aad7d9a21c49c07e924b9a531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ff58f671a287701011a1b31e67e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/eee2123a-b085-465b-a604-374e6bef3b4f.png?resizew=168)
(1)设点F为线段BC的中点,试证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若直线BE与平面ABC所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
您最近一年使用:0次
2023-09-19更新
|
2019次组卷
|
21卷引用:四川省凉山州宁南中学2023-2024学年高二上学期期末模拟数学试题(三)
四川省凉山州宁南中学2023-2024学年高二上学期期末模拟数学试题(三)四川省宜宾市第四中学校2023-2024学年高二上学期期末数学试题湖北省“荆、荆、襄、宜四地七校考试联盟2019-2020学年高三上学期10月联考数学(理)试题福建省厦门外国语学校2019-2020学年高三上学期12月月考数学(理)试题江西省新余市2019-2020学年高三上学期第四次段考数学(理)试卷福建师范大学第二附属中学2020届高三上学期期中考试数学(理)试题内蒙古霍林郭勒市第一中学2021-2022学年高二下学期期中考试数学试题河北省唐县第一中学2021-2022学年高二下学期期中数学试题陕西省宝鸡市虢镇中学2022-2023学年高三上学期第五次模考理科数学试题浙江省杭州市、宁波市部分学校2022-2023学年高三下学期4月联考数学试题(已下线)高二上学期期中【常考60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)重庆市涪陵区部分学校2023-2024学年高二上学期第一次月考数学试题广东省广州市第八十九中学2023-2024学年高二上学期10月月考数学试题重庆市广益中学校2023-2024学年高二上学期10月月考数学试题河南省开封市五县2023-2024学年高二上学期期中联考数学试题(已下线)第一次月考检测模拟试卷(原卷版)四川省成都市实验外国语学校2023-2024学年高二上学期第一阶段考试数学试题云南省大理州民族中学、怒江州民族中学2024届高三上学期第一次联合考试数学试题辽宁省沈阳市第十五中学2023-2024学年高二上学期12月月考数学试题四川省遂宁市蓬溪中学校2023-2024学年高二上学期12月月考数学试题北京市海淀区首都师范大学附属中学2023-2024学年高二上学期期中考试数学试题