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1 . 某校积极开展社团活动,在一次社团活动过程中,一个数学兴趣小组发现九章算术中提到了“刍薨”这个五面体,于是他们仿照该模型设计了一道数学探究题,如图1,E、F、G分别是边长为4的正方形的三边、
、
的中点,先沿着虚线段
将等腰直角三角形
裁掉,再将剩下的五边形
沿着线段
折起,连接
、
就得到了一个“刍甍”(如图2).
(1)若O是四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e826b8202fa0e17245dcc68426c923a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d786346b0e3f2d6666a2e7bf0b7e1251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7090ad13cf3664c89cdb2288779a9669.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770d42343599d3f26f0e0de8d5849f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8719c54c771e6c09d2219f90b844cc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2024-01-17更新
|
652次组卷
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3卷引用:山西省临汾市浮山中学校2023-2024学年高二下学期第一次月考数学试卷(A)
解题方法
2 . 在四面体
中,
,若四面体
的体积为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1656adca180d876a592e9b08831f3202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
A.二面角![]() ![]() |
B.二面角![]() ![]() |
C.![]() |
D.![]() ![]() |
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3 . 在平面直角坐标系中,设
、
,沿y轴把平面直角坐标系折成大小为
的二面角后,
,则
的弧度数为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/0e5120b7-43ba-413a-bba5-83fffa071aa6.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22340d6f2582502d69a5cb85f446ff43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/0e5120b7-43ba-413a-bba5-83fffa071aa6.png?resizew=175)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知
是直角三角形三边,
是斜边且
.且
的最小值为
.如图,在三棱锥
中,
,
两两垂直,
,则平面
与平面
所成角的夹角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e95c357d4846c8b8a2b13c1ac6f0287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43732e2f0cde5ffcc5878dc8de7a80f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8778533b6528aba7a1f19d80bbf4f880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/62c6327f-3138-4305-bca1-d7879330fcac.png?resizew=150)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 如图,在四棱锥
中,底面
是正方形,侧棱
底面
是
的中点,作
交
于点
.
(1)求证:
面
;
(2)求证:
平面
;
(3)求平面
与平面
的夹角的正弦值.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48dec2088f718b1d496e471ac96e281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.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://img.xkw.com/dksih/QBM/editorImg/2023/11/4/6a9e3026-ab5c-497f-8de5-c8194a80c509.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466fabcaac59132fea648ff35342ec9d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
6 . 如图,正方体的棱长为2,线段
上有两个动点
(
在
的左边),且
.下列说法错误的是( )
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() |
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2023-03-04更新
|
744次组卷
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6卷引用:山西省吕梁名师高级中学校2022-2023学年高二下学期开学考试数学试题
山西省吕梁名师高级中学校2022-2023学年高二下学期开学考试数学试题江苏省常州市前黄高级中学2022-2023学年高二下学期第一次学情检测数学试题河南省平顶山市等5地、舞钢市第一高级中学等2校2022-2023学年高二下学期开学考试数学试题(已下线)第6章 空间向量与立体几何 单元测试(B卷重难过关)-【学霸满分】2022-2023学年高二数学下学期重难点专题提优训练(苏教版2019选择性必修第二册)(已下线)高二上学期期中考试选择题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)3.4.3 求角的大小(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
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解题方法
7 . 如图,在正方体
中,
与
所成的角的大小;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bbdf5dbf9df96742624ada95c36146.png)
您最近一年使用:0次
2022-11-30更新
|
3488次组卷
|
9卷引用:山西省晋城市第一中学校(南岭爱物校区)2023-2024学年高二上学期11月月考数学试题
山西省晋城市第一中学校(南岭爱物校区)2023-2024学年高二上学期11月月考数学试题湖南省怀化市湖天中学2022-2023学年高二上学期9月月考数学试题(已下线)第09讲 拓展三:二面角的传统法与向量法(含探索性问题,7类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)黑龙江省大庆市大庆中学2023-2024学年高二上学期开学考试数学试题(已下线)第33讲二面角的几何求法第六章 立体几何初步(单元基础检测卷)第八章 立体几何初步(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(人教A版2019必修第二册)(已下线)第17讲 第八章 立体几何初步 章末重点题型大总结-【帮课堂】(人教A版2019必修第二册)(已下线)第8章 立体几何初步 单元综合检测(重点)-《重难点题型·高分突破》(人教A版2019必修第二册)
8 . 如图,在棱长为
的正方体
中,
、
分别是棱
、
上的动点,且
.
![](https://img.xkw.com/dksih/QBM/2022/9/27/3075680256434176/3077054814347264/STEM/a60d55b91b814c928cff229a2e11b70e.png?resizew=189)
(1)求证:
;
(2)当三棱锥
的体积取得最大值时,求平面
与平面
的夹角余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95628327dc58037e5368f4404c05ec39.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f8eebda19eded2b059774a8c2666c3.png)
![](https://img.xkw.com/dksih/QBM/2022/9/27/3075680256434176/3077054814347264/STEM/a60d55b91b814c928cff229a2e11b70e.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03022e8d9e2d2f962c6baa39463c6714.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5a44046c8232c8b81924036c6ba9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c878e789e07e33d65c8a18cf2c58a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
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2022-09-29更新
|
495次组卷
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6卷引用:山西省长治市名校联盟2021-2022学年高二下学期2月联考数学试题
9 . 已知四棱锥
中,底面
为等腰梯形,
,
,
,
是斜边为
的等腰直角三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/4400b9e4-0419-4e29-ab2a-826e48dee9d3.png?resizew=176)
(1)若
时,求证:平面
平面
;
(2)若
时,求直线
与平面
所成的角的正弦值.
![](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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641aa755ada1d83daafc82d5f1fa88db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b660bd8e98d065475eb0a1068cf2725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/4400b9e4-0419-4e29-ab2a-826e48dee9d3.png?resizew=176)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd63641dda745cf8917852d3e48fa70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b605cef1be4c42e0cb2d18bfc6f6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-06-13更新
|
683次组卷
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6卷引用:山西省大同市浑源中学2022-2023学年高二下学期期末数学试题
山西省大同市浑源中学2022-2023学年高二下学期期末数学试题(已下线)第4讲 空间向量的应用 (2)重庆市乌江新高考协作体2022-2023学年高二下学期期末数学试题浙江省长兴、余杭、缙云三校2022届高三下学期5月联考数学试题(已下线)7.3 空间角(精练)(已下线)第07讲 空间向量的应用 (2)
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10 . 如图,
是圆
的直径,点
是圆
上异于
,
的点,直线
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/cf64773d-a037-46c6-ab09-4036a5e13c24.png?resizew=175)
(1)证明:平面
平面
;
(2)设
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/22/cf64773d-a037-46c6-ab09-4036a5e13c24.png?resizew=175)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e0ba32fcadd4114a3c52b52c3aea23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4bddf1ea3c5d37f2233a4821909e9.png)
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