解题方法
1 . 如图,直四棱柱
的棱长均为
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/4740f9ce-ec7e-45b2-a227-22f02eff287f.png?resizew=162)
(1)求证:平面
平面
;
(2)若
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba964c27f118895f13672321aebe5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/4740f9ce-ec7e-45b2-a227-22f02eff287f.png?resizew=162)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803fa75db3ac3a26a41e347dc4165026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab181f6e579366c2c1f3e67e0d341b8.png)
您最近一年使用:0次
解题方法
2 . 如图
,在
中,
,
于
现将
沿
折叠,使
为直二面角
如图
,
是棱
的中点,连接
、
、
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/5cd64df1-3cc4-45b4-838b-0c01a40232f2.png?resizew=331)
(1)证明:平面
平面
;
(2)若
,且棱
上有一点
满足
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f4fac08d887c080386bf939bfdb4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470cb205a244f5a455d623e2dd72d622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af15dbf4a5abd508e8752bf3fd1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f9ad0f53f3813d148f16e532991021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f4fac08d887c080386bf939bfdb4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3701f73add38ffeb06fb42fef55fd533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad217e26bd3580c35998109de14cef73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/95226c64f0afdaa10b95ec097a0720ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a043206e1d0f1fc31e4edcb773746941.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/5cd64df1-3cc4-45b4-838b-0c01a40232f2.png?resizew=331)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8704811c9c5dba854310ae0de2ba6b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cfd630472bc73bd8c2209376dbe9d1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd270aed68cec28a22dff1cf891d8f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c2bb8c4f212a03496a8661deb2eb53.png)
您最近一年使用:0次
3 . 在四棱锥
中,底面
为直角梯形,
,侧面
底面
,且
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/9dd1c6bb-731a-4a7b-bd7f-f66d0c8fc966.png?resizew=173)
(1)证明:
平面
;
(2)若直线
与平面
所成的角为
,求平面
与平面
的夹角的余弦值.
![](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/68f0e48b7a6bb2836bffb57eaf2ff02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cff0c5518491ce9abc22c94a329041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa713e7c111c50a3404e12303fd6e0d2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/9dd1c6bb-731a-4a7b-bd7f-f66d0c8fc966.png?resizew=173)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
4 . 如图,在平行六面体
中,
,
,
,
,点
为
中点.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead0e8eadfdcefa334953e88864f424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7be9e552514a07e7f745666cb5b76b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b24a6fd9b4574e7808eafc57f8496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22391e2f16997bb4b99041f8543b2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104bf24922707215be95a860cd533940.png)
您最近一年使用:0次
2024-03-12更新
|
2933次组卷
|
9卷引用:辽宁省沈阳市五校联考2024届高三上学期期末数学试题
辽宁省沈阳市五校联考2024届高三上学期期末数学试题(已下线)每日一题 第16题 不易建系 先证垂直(高三)江西省宜春市丰城市第九中学2024届高三上学期期末考试数学试题(已下线)【一题多解】立体几何 新旧呼应湖南省长沙市雅礼中学2024届高三一模数学试卷江苏省常州市第一中学2024届高三下学期期初检测数学试题(已下线)专题04 立体几何辽宁省辽东十一所重点高中联合教研体2024届高三下学期高考适应性考试(一)数学试题(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题11-15
名校
5 . 如图,在四棱锥
中,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
,
是等边三角形,
为
的中点.
平面
;
(2)若
,求平面
与平面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ca23beefde179f4f91a0828c24a5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a30d398f116111502027bdcaef90f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991ec04fb924fd2407b679f56645126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2024-03-12更新
|
408次组卷
|
2卷引用:四川省成都外国语学校2023-2024学年高三上学期期末考试理科数学试题
解题方法
6 . 在四棱锥
中,底面ABCD是边长为2的菱形,
交
于O,
,
,
.
(1)求P到平面
的距离;
(2)求钝二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3eedeededdc7c9eb023aec9a101981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb7383ab3dc2ae9dce9b6ff0f8c4fb26.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/12/d083672e-6689-41c5-b467-9f21a3a6dd05.png?resizew=160)
(1)求P到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求钝二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
您最近一年使用:0次
名校
7 . 如图,在平行四边形
中,
,四边形
为正方形,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/894dab70-62b6-4329-86ae-709f7d0af0ba.png?resizew=160)
(1)证明:
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d524a7f82604044f8a27174c8e95e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/894dab70-62b6-4329-86ae-709f7d0af0ba.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f76925ed99b7172956319974258a9b.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,正方形
与梯形
所在的平面互相垂直,
,
,
,
,
为
的中点.
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2024-03-10更新
|
284次组卷
|
16卷引用:内蒙古自治区呼和浩特市土默特左旗第一中学2022-2023学年高一下学期期末数学试题
内蒙古自治区呼和浩特市土默特左旗第一中学2022-2023学年高一下学期期末数学试题江苏省八校2020-2021学年高一下学期5月期中联考数学试题2.4.2 空间线面位置关系的判定人教A版(2019) 选修第一册 第一章 空间向量与立体几何 章末达标检测卷人教A版(2019) 选修第一册 数学奇书 第一章 空间向量与立体几何 章末整合提升(已下线)1.4 空间向量应用(精讲)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)河北省衡水市武强县武强学校2023-2024学年高二上学期开学考数学试题宁夏石嘴山市平罗中学2023-2024学年高二上学期第一次月考数学试题(已下线)模块一 专题1 空间向量与立体几何(人教A)2(已下线)模块四 专题4 大题分类练 《空间向量与立体几何》基础夯实练上海市向明中学2023-2024学年高二上学期12月质量监控考试数学试卷(已下线)第一章 空间向量与立体几何(知识归纳+6类题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)专题05 用空间向量研究直线、平面的平行、垂直问题10种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)(已下线)第六章 空间向量与立体几何(压轴题专练)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第二册)(已下线)模块一 专题6《 空间向量应用》 A基础卷 (苏教版)(已下线)模块三 专题2 解答题分类练 专题4 空间向量的应用(苏教版)
9 . 如图,在正三棱柱
中,D,E分别为棱
的中点,
在棱
上,且EF
平面
.
(1)求
的值;
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79a03b1084cb2e8f8ac00329fe98544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/9/126fd3df-55c0-470f-8355-d5096437a597.png?resizew=138)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c8ae2f62d6a56f0ad6104814e73e50.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed487430a5b8a330f2d0c52166521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bff3ccea5989c60e51e321af3f53f54.png)
您最近一年使用:0次
10 . 如图,四棱台
的上、下底面均为正方形,
平面
.
(1)证明:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe349888317106ed511076fded08008.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/942b7cbe-27f0-411a-8f79-96f4408e6955.png?resizew=165)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2e84d6e368f8368f8301c4cd66d6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
您最近一年使用:0次