1 . 如图,四边形
为矩形,
在
上,且
,以
为折痕把
折起,使点
到达点
的位置,且
在平面
上的射影
在
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/335974c9-1ce0-4616-99cc-7d09af400ba8.png?resizew=282)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781b909f817216b4569c53bb7dc5f982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd75c2244c18120b8fc35d5d309ab66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/335974c9-1ce0-4616-99cc-7d09af400ba8.png?resizew=282)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cc33ee7afea61f57d8c5dc43e79596.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,底面
是平行四边形,
平面
,
是棱
上的一点,满足
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/1147598c-b995-4ba3-8bae-0bac67b22528.png?resizew=189)
(Ⅰ)证明:
;
(Ⅱ)设
,
,若
为棱
上一点,使得直线
与平面
所成角的大小为30°,求
的值.
![](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/5a1b49f64e0065edad868b25e9fcada3.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/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/1147598c-b995-4ba3-8bae-0bac67b22528.png?resizew=189)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec78c2154c5972efd438a6555afaf2d.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7794325335aa508186003c333e95ed5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb08a3eed3af2bdcb9d30e8b142de47f.png)
您最近一年使用:0次
2020-03-15更新
|
640次组卷
|
3卷引用:2020届内蒙古鄂尔多斯市第一中学高三下学期第一次模拟考试数学(理)试题
名校
解题方法
3 . 如图,在四棱锥
中,
底面ABCD,底面ABCD为梯形,
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a92932d5-fbb2-4d32-9c31-393b372e8196.png?resizew=168)
(1)在PD上是否存在一点F,使得
平面PAB,若存在,找出F的位置,若不存在,请说明理由;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facf189b2a3153beb7b9e077d3b1146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a86542e55ad35b90a5c7afd23e8803.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a92932d5-fbb2-4d32-9c31-393b372e8196.png?resizew=168)
(1)在PD上是否存在一点F,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350d224711c8773a7c5a2b34bf40bedc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2425afeae790f548529e24c81a40560c.png)
您最近一年使用:0次
2020-03-10更新
|
465次组卷
|
3卷引用:2020届甘肃省兰州市第二中学高三第五次月考理科数学试题
4 . 如图,三棱柱
中,
侧面
,已知
,
,
,点E是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/1941582f-9b4b-402d-a854-595f38408e1a.png?resizew=163)
(1)求证:
平面ABC;
(2)在棱CA上是否存在一点M,使得EM与平面
所成角的正弦值为
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec738fd1916032dff2b93f84f039404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7932b50fa677dfcd8e3b5061a90c133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/1941582f-9b4b-402d-a854-595f38408e1a.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ad7c180d6d084ecb25f23cb6fe9b10.png)
(2)在棱CA上是否存在一点M,使得EM与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914d46f7e72b55d2ff3d9bc38e02b31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0f4f8e3032f67e672b63791cc4d9df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7e6f1b753b73381b71eb5f8cc7da42.png)
您最近一年使用:0次
2020-03-10更新
|
1318次组卷
|
13卷引用:2020届广东省广州市执信中学高三2月月考数学(理)试题
2020届广东省广州市执信中学高三2月月考数学(理)试题2020届山东省济宁市嘉祥一中高三下学期第一次质量检测数学试题2020届陕西省西安市西北工业大学附中高三下学期4月适应性测试数学(理)试题广东省深圳市盐田区深圳外国语学校2021届高三上学期1月月考数学试题黑龙江省哈尔滨市第六中学2021届高三12月月考数学(理)试题广东省广州市执信中学2021届高三上学期第四次月考数学试题甘肃省嘉陵关市第一中学2020-2021学年高三下学期四模考试数学(理)试题四川省射洪中学校2020-2021学年高二上学期第三次月考数学(理)试题重庆实验外国语学校2020-2021学年高二下学期6月月考数学试题湖北省武汉市部分重点中学2021-2022学年高二上学期期中联考数学试题贵州省毕节市第一中学2021-2022学年高二上学期第二次阶段性考试数学(理)试题江苏省连云港市赣榆智贤中学2022-2023学年高二下学期3月学情检测数学试题湖北省武汉市华中科技大学附属中学2022-2023学年高二上学期9月月考数学试题
5 . 如图,在四棱锥
中,平面
平面
,
是边长为
的等边三角形,
,
,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6ca63356-1a83-49ff-96bd-fc8e57687d2a.png?resizew=190)
(1)求证:
平面
;
(2)求证:
;
(3)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecf025b484f24d1aef7e73a7a800105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c674dc5024374f53920947c4cf4baf11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3602ec4c8f5ac2737fa78c05708c869f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b405a122ded2eb0395d5434892ae7b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f64f78e151b46db08660df64a0c6132.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/2022/11/26/6ca63356-1a83-49ff-96bd-fc8e57687d2a.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ee5f3950aa6f59c76cf91c3ed8f290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051ca3c8e6421a0bd30620416468dd42.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d99c75180422fecf6d3f3d2910b34.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,四棱锥E﹣ABCD的侧棱DE与四棱锥F﹣ABCD的侧棱BF都与底面ABCD垂直,
,
//
,
.
![](https://img.xkw.com/dksih/QBM/2020/3/2/2410737436590080/2412398469545984/STEM/426907cc-7716-45c0-82c6-d9b05f14013e.png)
(1)证明:
//平面BCE.
(2)设平面ABF与平面CDF所成的二面角为θ,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.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/efdaef8d473c2deb6f4ca52e8fd9df0b.png)
![](https://img.xkw.com/dksih/QBM/2020/3/2/2410737436590080/2412398469545984/STEM/426907cc-7716-45c0-82c6-d9b05f14013e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)设平面ABF与平面CDF所成的二面角为θ,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
您最近一年使用:0次
2020-03-04更新
|
1221次组卷
|
7卷引用:2020届河南省高三上学期末数学理科试题
名校
解题方法
7 . 如图,四棱锥
中,
平面
,底面
是边长为2的正方形,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/b6f336f1-5b43-465d-ba2d-9b76fedb885f.png?resizew=157)
(1)求证:
;
(2)求二面角
的正弦值.
![](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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/b6f336f1-5b43-465d-ba2d-9b76fedb885f.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
您最近一年使用:0次
2020-02-27更新
|
336次组卷
|
4卷引用:2020届陕西省西安市高三年级第一次质量检测数学理科试题
2020届陕西省西安市高三年级第一次质量检测数学理科试题四川省泸州市泸县第五中学2020-2021学年高三上学期第一次月考数学(理)试题(已下线)专题09 法向量秒求-2021年高考数学二轮复习解题技巧汇总(新高考地区专用)黑龙江省哈尔滨市第三十二中学2020-2021学年高三上学期期末考试理科数学试题
解题方法
8 . 在直三棱柱
中,若
,
,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8e9ec412ea0355e4e5cd06c60e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af2626608f61a4cfbb86494bd6df0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-26更新
|
769次组卷
|
4卷引用:第30讲 长方体,四面体,旋转体模型-2022年新高考数学二轮专题突破精练
(已下线)第30讲 长方体,四面体,旋转体模型-2022年新高考数学二轮专题突破精练河南省安阳市滑县2019-2020学年高二上学期期末数学(理)试题辽宁省盘锦市第二高级中学2019-2020学年高二上学期期末考试数学试题四川省雅安市名山区第三中学2023-2024学年高二上学期12月月考数学试题
名校
9 . 如图1,在平行四边形
中,
=60°,
,
,
,
分别为
,
的中点,现把平行四边形
沿
折起如图2所示,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b5d693c4f0c4d0e6c0c810e7d464b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6cb992b6faad4744f85d73a3b76dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c2b3adb41e8965f553da2e5086a751.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a677b42f8b427b21924a559b90141d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44507c93f6180afd1697d2fa5a5c741.png)
您最近一年使用:0次
2021-06-15更新
|
1645次组卷
|
12卷引用:2016届福建福州市高三上学期期末数学(理)试卷
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名校
10 . 《九章算术》是我国古代数学名著,它在几何学中的研究比西方早1000多年,在《九章算术》中,将底面为直角三角形,且侧棱垂直于底面的三棱柱称为堑堵(qian du);阳马指底面为矩形,一侧棱垂直于底面的四棱锥,鳖膈(bie nao)指四个面均为直角三角形的四面体.如图在堑堵
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/1c2b2133-82d2-46e3-9b13-242ee0530f2c.png?resizew=176)
(1)求证:四棱锥
为阳马;
(2)若
,当鳖膈
体积最大时,求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/1c2b2133-82d2-46e3-9b13-242ee0530f2c.png?resizew=176)
(1)求证:四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0c82028e1259f300facd32775a15e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e43944426841fe584065908f677b192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ead078d0c9a22439c512767bf3d4c7.png)
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14卷引用:2020届山东省青岛市高三上学期期末数学试题
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