名校
1 . 如图,在四面体
中,
平面
,点
为棱
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/684dbcea-c0fd-4b1b-b9e6-b6df3d45eb70.png?resizew=150)
(1)证明:
;
(2)求平面
和平面
夹角的余弦值;
(3)在线段
上是否存在一点
,使得直线
与平面
所成角的正弦值为
?若存在,求
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b549fcb2b1bcdd843d9d7d9742ff1da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/684dbcea-c0fd-4b1b-b9e6-b6df3d45eb70.png?resizew=150)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9b10e4ec59b04c3322055be6a11cf7.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9b10e4ec59b04c3322055be6a11cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1145c162038df3c7184d9201c628e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747978ec67fee6ee9eb07d02b80987d7.png)
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2卷引用:北京市大兴区2023-2024学年高二上学期期末检测数学试题
解题方法
2 . 木楔在传统木工中运用广泛.如图,某木楔可视为一个五面体,其中四边形
是边长为2的正方形,且
均为等边三角形,
,
,则该木楔的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/97de503c-aca2-4922-8afc-f8bc68ed9222.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffb6bc33be59a39d0bf6530d02715b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451557ef624a9c142ebc5fa155e0e28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613dedf2d90e58591b7ac4a250ac7b5d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/7/97de503c-aca2-4922-8afc-f8bc68ed9222.png?resizew=163)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
3 . 如图1,在四边形
中,
,
.
,
分别为
,
的中点,
,
.将四边形
沿
折起,使平面
平面
(如图2)
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/aa4605f8-6c88-43b6-b96c-3645f36e4d24.png?resizew=325)
(1)证明:
.
(2)在线段
上是否存在一点
,使得
平面
?若存在,求
的值;若不存在,说明理由;
(3)证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c72dcde311e73cfd6fc3a664be8827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25f1b24ac2f6d3d63e3acffca9476f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5628323a7eeb11213df5c9048b3543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41c2d7ae6aaf6d91129ed5221a415a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/5/aa4605f8-6c88-43b6-b96c-3645f36e4d24.png?resizew=325)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5353af466bc30052c5a5669ecbcb79b4.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c623b8811d8cb0e8b32eb65229e478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1a983914cdbbbfe09d981adbb8a1d2.png)
(3)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ff58f671a287701011a1b31e67e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
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4 . 已知点P在棱长为2的正方体
表面运动,且
,则线段AP的长的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fee2699b73969f3059a987853a52aa6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-07-10更新
|
436次组卷
|
5卷引用:北京市大兴区2022-2023学年高一下学期期末检测数学试题
北京市大兴区2022-2023学年高一下学期期末检测数学试题(已下线)第13章 立体几何初步 章末题型归纳总结 (2)-【帮课堂】(苏教版2019必修第二册)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(2) -期期末真题分类汇编(北京专用)(已下线)专题08 几何体截面与展开最短距离归类(1) -期末考点大串讲(苏教版(2019))【北京专用】专题12立体几何与空间向量(第一部分)-高一下学期名校期末好题汇编
名校
解题方法
5 . 如图,在三棱锥
中,
和
都是等边三角形,点
为线段
的中点.
(1)证明:
;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求二面角
的余弦值.
①
;②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/2/e57135bc-b89d-419d-b522-a52f80769ca2.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)再从条件①、条件②这两个条件中选择一个作为已知,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7d6e5be7914a224e94a7b7e409a79c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585412bde1d2c7b297beaa78fd991130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa6dff1beaa6f6b8fdcb4ba496bac3b.png)
您最近一年使用:0次
2023-06-02更新
|
611次组卷
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2卷引用:北京大兴精华学校2023届高三高考适应性测试数学试题
6 . 如图1,四边形
是矩形,将
沿对角线
折起成
,连接
,如图2,构成三棱锥
.过动点
作平面
的垂线
,垂足是
.
落在何处时,平面
平面
,并说明理由;
(2)在三棱锥
中,若
为
的中点,判断直线
与平面
的位置关系,并说明理由;
(3)设
是
及其内部的点构成的集合,
,当
时,求三棱锥
的体积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f8441e5e499d705e4625e4c7db33dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8b40d14544a9be0bebdb276f0fa865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5933dbf3b867e009b26602dfbe0458e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ebf8aa867ccca195ec94c3c96e9b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)在三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfe1b2308c10e10cd8deaeddf9614a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e7281b475e016846062667edbd754e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172732c3b3e074a1f04599c355872fb3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9639896487e6cf18e8fd02d2a7ed2087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be73600a92d9b8eb472bad7b6acc334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
您最近一年使用:0次
2022-07-11更新
|
429次组卷
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5卷引用:北京市大兴区2021-2022学年高一下学期期末检测数学试题
北京市大兴区2021-2022学年高一下学期期末检测数学试题河北省赵县中学2022-2023学年高一下学期5月月考数学试题河北省石家庄市五校联合体2022-2023学年高一下学期期中数学试题(已下线)模块五 高一下期中重组篇(河北)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(2) -期期末真题分类汇编(北京专用)
名校
解题方法
7 . 如图,在四棱锥
中,
平面
,底面
为菱形,
分别为
,
的中点.
平面
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
平面
;
(3)若平面
平面
,求
的大小.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(3)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
您最近一年使用:0次
2022-07-11更新
|
846次组卷
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5卷引用:北京市大兴区2021-2022学年高一下学期期末检测数学试题
北京市大兴区2021-2022学年高一下学期期末检测数学试题(已下线)7.1 空间几何中的平行与垂直(精练)(已下线)7.2 空间几何中的垂直(精讲)四川省内江市第六中学2022-2023学年高一下学期第一次月考(创新班)数学试题(已下线)专题06 空间中点线面的位置关系6种常考题型归类(2) -期期末真题分类汇编(北京专用)
8 . 《九章算术·商功》:“斜解立方,得两壍堵(qiàn dǔ).斜解壍堵,其一为阳马,一为鳖臑(biē nào).阳马居二,鳖臑居一,不易之率也.”文中所述可用下图表示:
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848777216/STEM/8c0d64b8-e798-4905-a031-747276d8fa23.png?resizew=384)
则几何体“鳖臑”的四个面中,直角三角形的个数为_______ ;若上图中的“立方”是棱长为1的正方体,则
的中点到直线
的距离等于________ .
![](https://img.xkw.com/dksih/QBM/2022/1/14/2894203289747456/2895176848777216/STEM/8c0d64b8-e798-4905-a031-747276d8fa23.png?resizew=384)
则几何体“鳖臑”的四个面中,直角三角形的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
您最近一年使用:0次
名校
9 . 如图,已知正方体
中,
为线段
的中点,
为线段
上的动点,则下列四个结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887787316985856/2891584647790592/STEM/796bd250-15a4-4a92-ac5c-ec59f85d87ad.png?resizew=182)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2022/1/5/2887787316985856/2891584647790592/STEM/796bd250-15a4-4a92-ac5c-ec59f85d87ad.png?resizew=182)
A.存在点![]() ![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.直线![]() ![]() ![]() |
D.存在点![]() ![]() ![]() |
您最近一年使用:0次
2022-01-10更新
|
1615次组卷
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9卷引用:北京大兴精华学校2023届高三上学期12月月考数学试题
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名校
解题方法
10 . 如图,在三棱锥
中,
、
、
、
分别是
、
、
、
的中点,且
,
.
;
(2)证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67aca4db7d67c75ce68fe6912d17053d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
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