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1 . 在棱长为
的正方体
中,
、
两点在线段
上运动,且
,
在线段
上运动,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c096bd244d7e30e8ef26fb5278aac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
A.三棱锥![]() ![]() |
B.在平面![]() ![]() ![]() ![]() |
C.点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() ![]() |
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6卷引用:湖南省株洲市第一中学2022届高三上学期期末数学测试卷
湖南省株洲市第一中学2022届高三上学期期末数学测试卷江西省“三新”协同教研共同体2023-2024学年高二上学期12月联考数学试卷 江西省上饶市玉山县第二中学2024届高三上学期12月月考数学试题(已下线)结业测试卷(范围:第六、七、八章)(提高篇)-【寒假预科讲义】(人教A版2019必修第二册)(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点6 角度的范围与最值问题(一)【基础版】(已下线)第八章 立体几何初步(压轴题专练)-单元速记·巧练(人教A版2019必修第二册)
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2 . 在
中,
,
,
,如图所示,将
绕
逆时针旋转120°至
处,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/315b84b9-fa75-4442-8dc2-0016875a3d34.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19fc9f894312e55c87a0d6737080e233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86324ed305dbdaf5fcae861f2a2ffb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/24/315b84b9-fa75-4442-8dc2-0016875a3d34.png?resizew=162)
A.在旋转过程中,点![]() ![]() |
B.点![]() ![]() ![]() |
C.异面直线![]() ![]() |
D.直线![]() ![]() ![]() |
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2023-03-24更新
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4卷引用:湖南省长沙市宁乡市第一高级中学2021届高三第二次模拟考试数学试题
3 . 如图是一正方体的表面展开图,图中所示的四条线段在正方体中是异面关系且所成角为
的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
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4 . 三棱柱
中,棱长均为2,顶点
在底面
上的投影为棱
的中点,
为
的中点,
是
上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1264a2e3609e1c274acb89b5ea5019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cfad1ba71a78d8f415335cde2f8c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
A.三棱柱![]() | B.![]() ![]() ![]() |
C.![]() | D.异面直线![]() ![]() ![]() |
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2022-12-01更新
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1106次组卷
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4卷引用:湖南省株洲市第一中学2022届高三上学期期中数学试题
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5 . 已知A,B两点都在以PC为直径的球O的表面上,
,
,
,若球
的体积为
,则异面直线
与
所成角的余弦值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47eb6743075d149f8dc688aca72a00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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2023-08-09更新
|
743次组卷
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9卷引用:湖南省株洲市第一中学2021届高三第一次模拟检测数学试题
名校
解题方法
6 . 如图,在正方体
中,
分别为
的中点,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/aa7dc5c1-028c-485e-a9d6-1c974ab4be11.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3247c2d01d7fc107c00af21d5c33dba1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/aa7dc5c1-028c-485e-a9d6-1c974ab4be11.png?resizew=168)
A.![]() ![]() ![]() |
B.![]() |
C.直线![]() ![]() ![]() |
D.异面直线![]() ![]() ![]() |
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2022-06-21更新
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1190次组卷
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7卷引用:湖南省常德市第二中学2020-2021学年高二下学期期中数学试题
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7 . 四棱锥
,底面为正方形
,边
为
中点,
平面
.
(1)若
为等边三角形,求三棱锥
的体积;
(2)若
的中点为
与平面
所成角为
,求
与
所成角的正切值.
![](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/a1ba61f50c7429166adadf8fa21c3627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82867bb23bc067cce2848092c0222670.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6e5a7f3f5bf8e11ce978e69365578b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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解题方法
8 . 如图,平面四边形
中,
是等边三角形,
且
是
的中点.沿
将
翻折,折成三棱锥
,翻折过程中下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303653896192/STEM/3445b240-0268-42df-a6a4-92ec57df03e6.png?resizew=403)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8915e8e775538d41debf1933102c6b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ed50d0d07c007195a0263a57adbf3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303653896192/STEM/3445b240-0268-42df-a6a4-92ec57df03e6.png?resizew=403)
A.存在某个位置,使得![]() ![]() |
B.棱![]() ![]() ![]() ![]() ![]() |
C.当三棱锥![]() ![]() |
D.当二面角![]() ![]() ![]() |
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2022-06-04更新
|
2819次组卷
|
6卷引用:湖南师范大学附属中学2020-2021学年高一下学期期末数学试题
解题方法
9 . 如图,在棱锥
中,
为
的中点,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/84218c03-9f86-454b-907a-06d1265562a7.png?resizew=205)
(1)证明:
平面
;
(2)求异面直线
与
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.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/c86fa0c980a357a5b887b2eb9ce09f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83b76a280fc562446ee8ddd2d6bf1d4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/84218c03-9f86-454b-907a-06d1265562a7.png?resizew=205)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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10 . 如图是正方体的展开图,则在这个正方体中,正确命题的序号是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/3be544db-bb1e-4be2-a7b6-b9903837fa81.png?resizew=186)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/3be544db-bb1e-4be2-a7b6-b9903837fa81.png?resizew=186)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() |
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