名校
1 . 如图,在三棱柱
中,平面
平面
,
,四边形
是边长为
的菱形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/b041a252-99f7-430e-861c-0cdb28ddf14f.png?resizew=171)
(1)证明:
;
(2)若点
到面
的距离为
,求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6b781f45a00990af551427e5d81af2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/b041a252-99f7-430e-861c-0cdb28ddf14f.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba985fb50a9078a839b66bf1d1eadea9.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4fd5b13f66aaa25632811704596c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38be38165dc2307982fc57001a447c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410228a99ba57bb645b0bb857131535d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0c48ff2bc69a465c882a74bc806b8f.png)
您最近一年使用:0次
2022-05-31更新
|
1418次组卷
|
5卷引用:湖南省常德市桃源县第一中学2022-2023学年高三上学期9月月考数学试题
名校
2 . 已知△ABC是边长为6的等边三角形,点M,N分别是边AB,AC的三等分点,且
,
,沿MN将△AMN折起到
的位置,使
.
![](https://img.xkw.com/dksih/QBM/2022/3/21/2941122016854016/2941973344141312/STEM/2e8e1f2861954c9687b97882d744e8d7.png?resizew=424)
(1)求证:
平面MBCN;
(2)在线段BC上是否存在点D,使平面
与平面
所成锐二面角的余弦值为
?若存在,设
,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba486b7a12ec874644dc5fea93a56916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a45b6f1348711bc6eabd87982c3756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e7040c2fd8a163d71e35805775feb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d938067915b0d59f491b4c8ee7a982.png)
![](https://img.xkw.com/dksih/QBM/2022/3/21/2941122016854016/2941973344141312/STEM/2e8e1f2861954c9687b97882d744e8d7.png?resizew=424)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eedf1e774ce129d9a09f02ca1920052.png)
(2)在线段BC上是否存在点D,使平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4459d0d7b4c2e9e8106fe5b4520277e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c932cfbb9fb63159a176a8f45489a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e108d5c61e85e0741ec2c484fc5768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2f0857ee6d2e3e5341bcc916f2e067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-03-22更新
|
3708次组卷
|
7卷引用:湖南省常德市第一中学2022-2023学年高二下学期期中数学试题
名校
3 . 如图,四边形ABCD为梯形,
,
,
,点
在线段
上,且
.现将
沿
翻折到
的位置,使得
.
![](https://img.xkw.com/dksih/QBM/2022/3/2/2927482149060608/2936643822362624/STEM/f93ceca9-e75b-4c76-b3e0-ff9295997956.png?resizew=251)
(1)证明:
;
(2)点
是线段
上的一点(不包含端点),是否存在点
,使得二面角
的余弦值为
?若存在,则求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998329f9cdb86f5d60d7d5d70fc3781e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86752e4373797b2231f76b074cbf75d0.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/9b937442ad4cc480adc11bb143559454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe40405cd7bd60d69dd535d6da85c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbb42439079fa563100decbad833e10.png)
![](https://img.xkw.com/dksih/QBM/2022/3/2/2927482149060608/2936643822362624/STEM/f93ceca9-e75b-4c76-b3e0-ff9295997956.png?resizew=251)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbfbaf73297240eb116f22489519895a.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98553247801c03de24cf7e687016e655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d6d600e2676abc87e05cde8aebc1a.png)
您最近一年使用:0次
2022-03-15更新
|
3284次组卷
|
9卷引用:湖南省常德市临澧县第一中学2021-2022学年高三下学期第九次阶段性考试数学试题
4 . 如图,在四棱台
中,底面为矩形,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712438274220032/2714554383310848/STEM/122c1456-e78f-4279-bcd1-27f76d1150cd.png?resizew=267)
(1)证明:
平面
;
(2)若
与平面
所成角为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6b6b19c079b935283768502ff7eb13.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712438274220032/2714554383310848/STEM/122c1456-e78f-4279-bcd1-27f76d1150cd.png?resizew=267)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321c26a8d3d434112c79465631f5629c.png)
您最近一年使用:0次
2021-05-05更新
|
2476次组卷
|
10卷引用:湖南省常德市临澧县第一中学2020-2021学年高二下学期期末数学试题
湖南省常德市临澧县第一中学2020-2021学年高二下学期期末数学试题湖南省2021届高三下学期三模数学试题全国Ⅱ卷决胜高考2021届高三数学(理)仿真卷试题(六)(已下线)专题06 空间向量与立体几何(难点)-2020-2021学年高二数学下学期期末专项复习(北师大版2019选择性必修第一册、第二册)(已下线)第20题 立体几何解答题的两大主题:线面位置的证明及空间角-2021年高考数学真题逐题揭秘与以例及类(新高考全国Ⅰ卷)(已下线)专题04 空间向量与立体几何的压轴题(二)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)江苏省南京市江宁高级中学2022届高三下学期适应性考试数学试题福建省厦外石狮分校、泉港一中两校联考2023届高三上学期第二次月考数学试题福建省厦门外国语学校石狮分校2022-2023学年高二上学期期中考试数学试题重庆市长寿中学2022-2023学年高三下学期3月月考数学试题
名校
解题方法
5 . 已知梯形
中,
,
,
,
,
分别是
,
上的点,
,
,沿
将梯形
翻折,使平面
平面
(如图).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/0966c234-3aa3-4983-99d6-65cfbaf4312e.png?resizew=309)
(1)当
时,①证明:
平面
;②求二面角
的余弦值;
(2)三棱锥
的体积是否可能等于几何体
体积的
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d3947804a878a87052c266be475423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fcb0ab3b6099434e4cdde2ea871f3f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/9d459cad63e3cd2aba10862800fa4832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c30f73c718bde8352055a14987fc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d8c77f758b4a06c320be39ecb328f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e826b8202fa0e17245dcc68426c923a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/0966c234-3aa3-4983-99d6-65cfbaf4312e.png?resizew=309)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febe72169c8dd4ecb57eadf7256dcbeb.png)
(2)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67445ee86986aa474e8d71641d46b2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b575beb309541b02c629700b21e9c8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d86ab7c97cd8a0b15ba5efc1be94230.png)
您最近一年使用:0次
2020-08-16更新
|
1417次组卷
|
7卷引用:湖南省常德市临澧县第一中学2023-2024学年高二下学期入学考试数学试题
6 . 如图,已知三棱柱
的侧棱垂直于底面,
,
,点
,
分别为
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/23400cdf-6e8e-4b56-aeaf-5954342cf0fe.png?resizew=158)
(1)若
,求三棱柱
的体积;
(2)证明:
平面
;
(3)请问当
为何值时,
平面
,试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8684078379a9e6b209068e1de693af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.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/9806df6df27bf715c81c4a93fc6517c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f3cbee923ebf5179770f7dbb53b38f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/23400cdf-6e8e-4b56-aeaf-5954342cf0fe.png?resizew=158)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c15dd981c5b6dbfd5b3f6462a624b83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8684078379a9e6b209068e1de693af0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63515a3fe55a14fa7f87dfc1ed9626ee.png)
(3)请问当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e416ca9e681b92c492cfedfa19b05e40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd97452bd150c579f4fb571a85e12cfa.png)
您最近一年使用:0次
7 . 《九章算术》中,将底面为长方形且有一条侧棱与底面垂直的四棱锥称之为阳马,将四个面都为直角三角形的四面体称之为鳖臑.
如图,在阳马
中,侧棱
底面
,且
,过棱
的中点
,作
交
于点
,连接 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9239dd73df715a39ae6f3f69f14a92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/fdfbbd24-8548-41c1-8788-6c0994e50143.png?resizew=175)
(Ⅰ)证明:
.试判断四面体
是否为鳖臑,若是,写出其每个面的直角(只需写
出结论);若不是,说明理由;
(Ⅱ)若面
与面
所成二面角的大小为
,求
的值.
如图,在阳马
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/37e2267c84394668eff2e9f5918de4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9239dd73df715a39ae6f3f69f14a92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/fdfbbd24-8548-41c1-8788-6c0994e50143.png?resizew=175)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017797398acdf601fd6f40b1e20e8751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc50ecfa45216f8d098662452cf8d08.png)
出结论);若不是,说明理由;
(Ⅱ)若面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54625f5af5647c5dad88675510c4711b.png)
您最近一年使用:0次
2016-12-03更新
|
5718次组卷
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31卷引用:湖南省常德市临澧县第一中学2023-2024学年高二上学期第一次阶段性考试数学试题
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2014·湖南·二模
8 . 如图,在四棱锥
中,
平面
,
,且
,
,
,点
在
上.
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572452507246592/1572452513316864/STEM/0e878378d5bd4d9bbb7d9dc88caa3e2f.png?resizew=253)
(1)求证:
;
(2)若二面角
的大小为
,求
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1750703a4d8ad6595e9ac955d27742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2478a116f8ff83c8477094e97c4211cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2016/1/20/1572452507246592/1572452513316864/STEM/0e878378d5bd4d9bbb7d9dc88caa3e2f.png?resizew=253)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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