名校
解题方法
1 . 下列命题正确的有( )
A.空间中两两相交的三条直线一定共面 |
B.已知不重合的两个平面![]() ![]() ![]() |
C.有两个平面平行,其他各个面都是平行四边形的多面体是棱柱 |
D.过平面![]() ![]() ![]() ![]() |
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名校
2 . 已知不重合的直线l,m和不重合的平面
,
,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() ![]() ![]() |
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2023-04-26更新
|
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11卷引用:湖北省襄阳东风中学2022-2023学年高二上学期9月月考数学试题
湖北省襄阳东风中学2022-2023学年高二上学期9月月考数学试题浙江省台州市2020-2021学年高一下学期期末数学试题浙江省衢州市乐成寄宿中学2021-2022学年高一下学期期中数学试题浙江省台州市第一中学2022-2023学年高一下学期期中数学试题浙江省长河高级中学2022-2023学年高一下学期期中数学试题(已下线)6.5.1直线和平面垂直(课件+练习)(已下线)专题09 空间直线与平面的垂直问题 -期中期末考点大串讲广东省广州市第一一三中学2022-2023学年高一下学期阶段二考试(5月)数学试题天津市第四十二中学2022-2023学年高一下学期5月月考数学试题宁夏六盘山高级中学2022-2023学年高一下学期第二次月考数学试题甘肃省白银市靖远县第四中学2022-2023学年高一下学期6月月考数学试题
名校
解题方法
3 . 图1中,正方体
的每条棱与正八面体
(八个面均为正三角形)的条棱垂直且互相平分.将该正方体的顶点与正八面体的顶点连结,得到图2的十二面体,该十二面体能独立密铺三维空间.若
,则点M到直线
的距离等于( )
![](https://img.xkw.com/dksih/QBM/2023/3/8/3190273070194688/3190747430830080/STEM/1c5fcbfd0978478caa02fcef2b99e347.png?resizew=380)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32cc86e0674d47374e41ee4725aec8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd02e391a3cc06af4a9df86041d816b7.png)
![](https://img.xkw.com/dksih/QBM/2023/3/8/3190273070194688/3190747430830080/STEM/1c5fcbfd0978478caa02fcef2b99e347.png?resizew=380)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-03-09更新
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905次组卷
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2卷引用:湖北省襄阳市第五中学2023届高三下学期适应性考试(一)数学试题
4 . 如图,三棱锥
的底面
是直角三角形,
,
,
平面
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/25be8e8a-2402-4b2c-b6ef-760703e9096c.png?resizew=125)
(1)若此三棱锥的体积为
,求异面直线
与
所成角的大小.
(2)若
,
①求点
到平面
的距离.
②过点
作平面
与平面
垂直,且和直线
平行,求平面
截三棱锥
的截面的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79faaf0e895a5e3edf40756d990e1161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd654221ab95fe241d9e0202443f2609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/25be8e8a-2402-4b2c-b6ef-760703e9096c.png?resizew=125)
(1)若此三棱锥的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031661aa4b14c3b9954ec444ad5b6f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d3f5f4c4419913c1232b7aae03ade.png)
②过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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5 . 如图,在棱长为1的正方体
中,P为线段
上不与A,
重合的动点,则下列选项中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/aa3fa8de-e183-4455-86a6-f93679c7f219.png?resizew=172)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/aa3fa8de-e183-4455-86a6-f93679c7f219.png?resizew=172)
A.异面直线CP与![]() ![]() |
B.当点P运动时,平面![]() ![]() |
C.当点P运动时,三棱锥![]() |
D.当点P运动时,![]() ![]() |
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2022-01-26更新
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3卷引用:湖北省襄阳市2021-2022学年高二上学期元月期末数学试题
6 . 蹴鞠(如图所示),又名蹴球,蹴圆,筑圆,踢圆等,蹴有用脚蹴、踢、蹋的含义;鞠最早系外包皮革、内实米糠的球.因而蹴鞠就是指古人以交蹴、蹋、踢皮球的活动,类似于今日的足球.早在2006年5月,蹴鞠已作为非物质文化遗产经国务院批准列入第一批国家非物质文化遗产名录.现已知某蹴鞠的表面上有四个点
、
、
、
,满足
是正三棱锥,
是
的中点,
,侧棱长为2,则该蹴鞠的体积为________ ;蹴鞠球心到平面
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23fb7f88bd587b02398f7cccc938c994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/19967353-3d95-4545-bafa-10c6aa294736.png?resizew=100)
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3卷引用:湖北省襄阳市第四中学2021-2022学年高一下学期5月月考数学试题
名校
解题方法
7 . 如图是第七届国际数学教育大会的会徽,它的主题图案由一连串如图所示的直角三角形演化而成.设其中的第一个直角
.是等腰三角形,且
,则
,
,…,
,现将
沿
翻折成
,则当四面体
体积最大时,它的表面有___________ 个直角三角形;当
时,四面体
外接球的体积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15536798ab47cadce6d4d80f542051f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74895fb6d64f400bbf2ebf9f8eab7a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bd53050136a720676adb5e2d752b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce7c3b13d76958eb370bad0003e3357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e095d18f60bd29ab93614dee47cc13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15536798ab47cadce6d4d80f542051f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c76916c6ff302cf4fb4b6ace5bb3a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fac9edcf08eabbd352169552860eb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776e703f82e0077ee54a84641bdbeb4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d3068dc3f5dd1355f31df1e3ff0204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/776e703f82e0077ee54a84641bdbeb4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/ab6535bd-47a8-4b77-856e-baee031d3ab8.png?resizew=384)
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3卷引用:湖北省襄阳市部分优质高中2020-2021学年高三上学期2月联考数学试题
解题方法
8 . 如图正方体
的棱长为2,线段
,上有两个动点E,F,且
,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/d99b7e83-8169-498c-87f5-6e226c187758.png?resizew=133)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/d99b7e83-8169-498c-87f5-6e226c187758.png?resizew=133)
A.![]() |
B.![]() ![]() |
C.三棱锥![]() ![]() |
D.![]() ![]() |
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解题方法
9 . 如图三棱柱,
为菱形,
,
,
为
的中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d142a27b-c168-42fe-8589-fd46fd7bcb72.png?resizew=179)
(1)求证:
;
(2)若
,
,求二面角
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040bece4d468e2353832b1cbe35d9dfd.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/c8d3a3f9bae62377ff6e18e7d94e21d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d142a27b-c168-42fe-8589-fd46fd7bcb72.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5485a6bc3ba67f92a37d38a15d515a25.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cad94a7ce4b201a9e95674e19d828d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5983c84ac412b4683ed0dc664883177.png)
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解题方法
10 . 如图,等边三角形
的中线
与中位线
相交于
,已知
是
绕
旋转过程中的一个图形,下列命题中,正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/29b1502f-fdfa-4638-8fcd-3adb16f00732.png?resizew=208)
①恒有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37682b4c45a8a00c96098382a80944df.png)
②异面直线
与
不可能垂直
③恒有平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
④动点
在平面
上的射影在线段
上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e92fed536087a6c2e8c44296b81a1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a4feb150ad9cff8d70431c97eb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/29b1502f-fdfa-4638-8fcd-3adb16f00732.png?resizew=208)
①恒有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37682b4c45a8a00c96098382a80944df.png)
②异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968b886a9f161fdcab1e08cba8ece5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
③恒有平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b8b05158b9e0550af222ed85c35902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
④动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-04-30更新
|
190次组卷
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2卷引用:湖北省襄阳市第四中学2019-2020学年高一下学期4月月考数学试题