1 . 如图,五面体
的底面
是矩形,
∥底面
,
到底面
的距离为1,
.
平面
;
(2)设平面
平面
.
①证明:
底面
;
②求
到底面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9eb9126c7053574c62b897582ad49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c20bda518870f0e27a5c1636206458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6290c9cefc2a4c5fa2325f80cb4863b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48abba67b697688749cf92b8c7205161.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
您最近一年使用:0次
名校
解题方法
2 . 一副标准规格的三角板按图(1)方式摆放构成平面四边形
,
,
为
的中点.将
沿
折起至
,连接
,使得
,如图(2).
(1)证明:平面
平面
.
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520f8abda6a85e7ef6f281fc2df853fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a1983972735c6bd98bfbe115bb2437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e78042a384255038de485fd7bc0839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174471d56bb8989b12bfc03ef74d54cd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/12/065b71d4-8739-4762-b0ed-a8354afc92f3.png?resizew=301)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
解题方法
3 . 在正三棱柱
中,底面ABC是边长为2的等边三角形,
,D为BC中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
A.平面![]() ![]() |
B.异面直线![]() ![]() |
C.点M在![]() ![]() ![]() |
D.设P,Q分别在线段![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-07-04更新
|
812次组卷
|
4卷引用:安徽省太和中学2022-2023学年高二上学期数学竞赛试卷
安徽省太和中学2022-2023学年高二上学期数学竞赛试卷江苏省泰州市2021-2022学年高二下学期期末数学试题(已下线)第03讲 空间向量及其运算的坐标表示(7大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)【江苏专用】专题10立体几何与空间向量(第二部分)-高二下学期名校期末好题汇编
名校
解题方法
4 . 如图,圆台上底面圆
半径为1,下底面圆
半径为
为圆台下底面的一条直径,圆
上点
满足
是圆台上底面的一条半径,点
在平面
的同侧,且
.
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966573292437504/2968469579579392/STEM/259d8c83-f08f-4c4b-9aef-f05e35c1d544.png?resizew=163)
(1)证明:平面
平面
;
(2)若圆台的高为2,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838a424964c2e96bb8e8dfc27a062b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46827c30d924e9a7fc8d627515e4c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaa712e64750e3e2843bae68ebad6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3da630440d6d416f19ee22c8431c882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b658c6aaa010f64b703a97b3fc7db187.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966573292437504/2968469579579392/STEM/259d8c83-f08f-4c4b-9aef-f05e35c1d544.png?resizew=163)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若圆台的高为2,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee51552e3c12bc27cf8ab1777bf191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-04-29更新
|
2925次组卷
|
9卷引用:湖南省湘西州吉首市2022年第一届中小学生教师解题大赛数学试题
名校
解题方法
5 . 如图,四棱锥
中,底面ABCD为矩形,平面
平面ABCD,
,
,E,F分别为AD,PB的中点.求证:
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882847899779072/2920000285032448/STEM/8c22064922c74549955b4ec103b2c53f.png?resizew=242)
(1)
∥平面PCD;
(2)平面
平面PCD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/2021/12/29/2882847899779072/2920000285032448/STEM/8c22064922c74549955b4ec103b2c53f.png?resizew=242)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
您最近一年使用:0次
2022-02-19更新
|
775次组卷
|
6卷引用:安徽省太和中学2022-2023学年高二上学期数学竞赛试卷
名校
解题方法
6 . 如图,已知四棱锥
的底面
是平行四边形,
,
,
,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
底面
,直线
与底面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/87c83e5c-68d3-4999-9b5b-a1defbf9a3c0.png?resizew=217)
(1)证明:平面
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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae16b72924eb24c45f5dcfab07cc01b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/87c83e5c-68d3-4999-9b5b-a1defbf9a3c0.png?resizew=217)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
7 . 如图,在四棱锥
中,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869d3b18732c9b4b42887d003d7c497b.png)
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/7/12/1572916675854336/1572916681998336/STEM/219ab4b1758049db989d579ba3582596.png?resizew=146)
(Ⅰ)求证:平面
⊥平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413c799e8fb983e6274ec4be9ff6c431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869d3b18732c9b4b42887d003d7c497b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29470a095de205acb450d5a48b38be1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acb69f52b245011a41daaefd5b2a316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d97afe2733b75e9ea3de65c882f851c.png)
![](https://img.xkw.com/dksih/QBM/2016/7/12/1572916675854336/1572916681998336/STEM/219ab4b1758049db989d579ba3582596.png?resizew=146)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-04更新
|
1634次组卷
|
9卷引用:第十四届高二试题(A卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)