名校
1 . 在正方体
中,设
,
分别为棱
,
的中点.
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/fc6f5cea-c0a1-4843-b639-057813855140.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7513c5dc6e1d35f76020f8f60c95669.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4408bbbd7d295e7b3900e53d70f28543.png)
您最近一年使用:0次
2023-10-13更新
|
498次组卷
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6卷引用:广东省惠州市龙门县高级中学2023-2024学年高二上学期期中数学试题
广东省惠州市龙门县高级中学2023-2024学年高二上学期期中数学试题江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省淮安市马坝高级中学2023-2024学年高三上学期10月学情调研测试数学试题重庆市九龙坡区杨家坪中学2023-2024学年高二上学期第二次月考数学试题(已下线)专题09 立体几何(5大易错点分析+解题模板+举一反三+易错题通关)-2
名校
2 . 如图,在四棱锥
中,底面
为正方形,侧面
是正三角形,侧面
底面
,
是
的中点.
平面
;
(2)求侧面
与底面
所成二面角的余弦值.
![](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/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-07-08更新
|
1812次组卷
|
8卷引用:广东省惠州市2022-2023学年高一下学期期末数学试题
3 . 如图,三棱锥
中,
,
.
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de13256f52663ee5809a964eb28725bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1385c59d0fe2bc62fed70a2d13a5e956.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/f322246c-e0e0-48b4-aef3-4736c5de432f.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99116c812715c5e15ee73d088da4c253.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5768a8d6630375daf58e971fa200c5.png)
您最近一年使用:0次
2023-07-05更新
|
347次组卷
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2卷引用:广东省惠州市惠东县惠东荣超中学2023-2024学年高二上学期开学考试数学试题
名校
4 . 如图,在五面体
中,
平面ABC,
,
,
.
(1)问:在线段CD上是否存在点P,使得
平面ACD?若存在,请指出点P的位置,并证明;若不存在,请说明理由.
(2)若
,
,
,求平面ECD与平面ABC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfa223e7b272346649538457c976864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d379ef9a50ae13b4264559ddd64da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/120d431c-bfa9-4823-b559-26da02f9eb82.png?resizew=168)
(1)问:在线段CD上是否存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
您最近一年使用:0次
2023-07-05更新
|
764次组卷
|
3卷引用:广东省惠州市2024届高三上学期第一次调研数学试题
解题方法
5 . 如图,在五面体
中,
为边长为2的等边三角形,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986450005155840/2987913093324800/STEM/0ddad4f1c446458fbd14bab8ffa86ef9.png?resizew=174)
(1)求证:平面
平面
;
(2)若直线
与平面
所成角的正切值为
,求平面BDE与平面ABC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cea1fa98ed569e4e0e51df9e536da18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e52afb0eaa29b2e542805716db11243.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986450005155840/2987913093324800/STEM/0ddad4f1c446458fbd14bab8ffa86ef9.png?resizew=174)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
您最近一年使用:0次
6 . 如图,在四棱锥
中,底面
是边长为2的菱形,
,
,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981467014750208/2982704202211328/STEM/c866f5d7-1d48-40aa-a887-7dd18526b217.png?resizew=162)
(1)证明:平面
平面
;
(2)若Q为棱
上一点,且
,求二面角
的大小.
![](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/1bae7599ad243c12d94325ad917f0a44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755b2bcf7516eedb26a27ad73657216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981467014750208/2982704202211328/STEM/c866f5d7-1d48-40aa-a887-7dd18526b217.png?resizew=162)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若Q为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4fc0b2955d06fbb4e5f2dd047c253f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ea10539215794cd76e8b211abd503f.png)
您最近一年使用:0次
2022-05-19更新
|
994次组卷
|
3卷引用:广东省惠州市博罗县榕城中学2021-2022学年高一下学期第二次月考数学试题
名校
7 . 在四棱锥
中,底面ABCD是菱形,
,
平面ABCD,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/0b8ff67d-f743-4128-acf5-3928c2b0d02f.png?resizew=164)
(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/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/0b8ff67d-f743-4128-acf5-3928c2b0d02f.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
您最近一年使用:0次
2022-05-12更新
|
552次组卷
|
3卷引用:广东省惠州市华罗庚中学2022-2023学年高二下学期3月月考数学试题
解题方法
8 . 近年来,纳米晶的多项技术和方法在水软化领域均有重要应用.纳米晶体结构众多,下图是一种纳米晶的结构示意图,其是由正四面体沿棱的三等分点作平行于底面的截面得到所有棱长均为n的几何体,则下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/a42cfc20-4d2a-46c6-8848-459000c6524f.png?resizew=184)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/a42cfc20-4d2a-46c6-8848-459000c6524f.png?resizew=184)
A.该结构的纳米晶个体的表面积为![]() |
B.该结构的纳米晶个体的体积为![]() |
C.该结构的纳米晶个体外接球的表面积为![]() |
D.二面角A1−A2A3−B3的余弦值为![]() |
您最近一年使用:0次
名校
9 . 如图所示,从一个半径为
(单位:
)的圆形纸板中切割出一块中间是正方形,四周是四个正三角形的纸板,以此为表面(舍弃阴影部分)折叠成一个正四棱锥
,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7affd362b4b1b24ac16f5af57822a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
A.四棱锥![]() ![]() |
B.四棱锥![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.二面角![]() ![]() |
您最近一年使用:0次
2021-11-02更新
|
2164次组卷
|
5卷引用:广东省惠州市2022届高三上学期第二次调研(10月)数学试题
10 . 如图,已知四边形
为直角梯形,
,
,
,
,且平面
平面
,
是边长为2的等边三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/184975b5-a998-45a0-a4ec-c58f98191141.png?resizew=212)
(1)证明:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e306e30d3159e4a68435c3fcfc8da693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ad6a0124359e8b9f7649cf0bff51ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/184975b5-a998-45a0-a4ec-c58f98191141.png?resizew=212)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9e5f1cfea3643c30c21732073a11ef.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479b251fdb01bae6d16abb7f2d694a7.png)
您最近一年使用:0次