21-22高一·湖南·课后作业
解题方法
1 . 如图,已知四棱锥
的底面为直角梯形,
,
,且
,
.
(2)求证:平面
平面ABCD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
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6卷引用:10.4 平面与平面间的位置关系(第1课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)
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13-14高三上·甘肃·阶段练习
2 . 如图,已知四棱锥
的底面为直角梯形,
,
,
,
.
与平面
不垂直;
(2)证明:平面
平面
;
(3)如果
,二面角
等于
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96f0e183dc8133ad2639368cf9436463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
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8卷引用:上海市复旦中学2023-2024学年高二上学期期末考试数学试卷
上海市复旦中学2023-2024学年高二上学期期末考试数学试卷(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)(已下线)2014届甘肃西北师大附中高三11月月考理科数学试卷(已下线)2014届甘肃省西北师大附中高三11月月考理科数学试卷(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)(已下线)第13章 立体几何初步 单元综合检测(重难点)-《重难点题型·高分突破》(苏教版2019必修第二册)(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)
解题方法
3 . 如图①,在棱长为1的正方体
中,E是棱
上的一个动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/27eb5ee9-401d-49e1-9d22-71c8990bbc40.png?resizew=320)
(1)求证:三棱锥
的体积是定值;
(2)是否存在点E,使得
平面
,若存在请找出点E的位置,若不存在,说明理由;
(3)定义:与两条异面直线都垂直且相交的直线称为这两条异面直线的公垂线,公垂线的两个垂足之间的线段称为异面直线的公垂线.两条异面直线的公垂线段,是连接两条异面直线所有线段中的最短线段.
根据以上定义及性质解决如下问题:
如图②中,M为线段
的中点,线段
(不包括两个端点)上有一个动点N,过点
、
、
作正方体的截面
.
①判断截面
的形状,并说明理由;
②当截面
的面积取得最小值时,求点N的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/27eb5ee9-401d-49e1-9d22-71c8990bbc40.png?resizew=320)
(1)求证:三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bcd4d16a1f2e89bb43fd1731a05ab1.png)
(2)是否存在点E,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
(3)定义:与两条异面直线都垂直且相交的直线称为这两条异面直线的公垂线,公垂线的两个垂足之间的线段称为异面直线的公垂线.两条异面直线的公垂线段,是连接两条异面直线所有线段中的最短线段.
根据以上定义及性质解决如下问题:
如图②中,M为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①判断截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②当截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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解题方法
4 . 在边长为
的正方形
中,
分别为
、
的中点,
分别为
、
的中点,现沿
、
、
折叠,使
三点重合,重合后的点记为
,构成一个三棱锥.
![](https://img.xkw.com/dksih/QBM/2023/10/19/3349137315151872/3349529531162624/STEM/690623105f0f46ef858000c0869a746c.png?resizew=320)
(1)请判断
与平面
的位置关系,并给出证明;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a11e8c4c6bfbf140ee21f99c0b5e6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f223740ec3b688a7a55c06ec8b57d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2023/10/19/3349137315151872/3349529531162624/STEM/690623105f0f46ef858000c0869a746c.png?resizew=320)
(1)请判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb30211c56375a3901fc098174672e5f.png)
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5 . 如图,梯形ABCD所在的平面与等腰梯形ABEF所在的平面互相垂直,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/065866ec-1b4a-41df-834b-0776fd60bf14.png?resizew=257)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
平面BCE;
(2)求二面角
的余弦值;
(3)线段CE上是否存在点G,使得
平面BCF?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c75d8581bb7b2a91795852acdc07d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4ea681be3e312f3aab464cebf3e0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dfc9d1109fe41145cc892b5702d9fb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/065866ec-1b4a-41df-834b-0776fd60bf14.png?resizew=257)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d6b07f069d2d823c04b0e53dabd925.png)
(3)线段CE上是否存在点G,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071159cac13097ea0928285bc1be66d8.png)
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13卷引用:上海市进才中学2017-2018学年高二下学期期末数学试题
上海市进才中学2017-2018学年高二下学期期末数学试题【全国百强校】天津市耀华中学2018届高三年级第二次模拟考试数学(理)试题【百强校】云南省玉溪一中2018-2019学年高二上学期期末考试数学理试题四川省乐山市2019-2020学年高二上学期期末数学(理)试题广东省广州市第八十九中学2021-2022学年高二上学期第一次月考数学试题北京市中央民族大学附属中学2022届高三12月月考数学试题重庆市暨华中学校2021-2022学年高二上学期10月月考数学试题(已下线)易错点10 立体几何-备战2022年高考数学考试易错题(新高考专用)北京市育才学校2022届高三下学期仿真测试数学试题北京市第二中学2022-2023学年高二下学期第六学段(期末)考试数学试题广东省广州市培英中学2023-2024学年高二上学期10月月考数学试题(已下线)北京市第四中学2023~2024学年高二上学期期中考试数学试题黑龙江省哈尔滨市第四中学校2023-2024学年高二上学期11月月考数学试题
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解题方法
6 . 已知正方体
的棱长为a,E、F分别为棱
、
的中点,P为体对角线
所在直线上一动点.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878865860804608/2879476422508544/STEM/04f5074ad4af4ca68c62db8b5f99a97d.png?resizew=226)
(1)作出该正方体过点E、F且和直线
垂直的截面,并证明该截面和直线
垂直;
(2)求出△EFP绕直线EF旋转而成的几何体体积的最小值;
(3)若动点M在直线EF上运动,动点N在平面
上运动,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878865860804608/2879476422508544/STEM/04f5074ad4af4ca68c62db8b5f99a97d.png?resizew=226)
(1)作出该正方体过点E、F且和直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
(2)求出△EFP绕直线EF旋转而成的几何体体积的最小值;
(3)若动点M在直线EF上运动,动点N在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bb1548ddc0e5536a35b1bd78c4e7cd.png)
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3卷引用:上海市奉贤中学2021-2022学年高二上学期12月月考数学试题
上海市奉贤中学2021-2022学年高二上学期12月月考数学试题(已下线)第05讲线线、线面、面面垂直的判定与性质(核心考点讲与练)(2)河南省安阳市第一中学2021-2022学年高一下学期第二次阶段考试数学试题
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7 . 已知四棱锥
的底面
为菱形,且
,
,
,
与
相交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/1180cd27-53de-4a5a-a91b-f512b407ca67.png?resizew=186)
(1)求证:
底面
;
(2)求直线
与平面
所成的角
的值;
(3)求平面
与平面
所成二面角
的值.(用反三角函数表示)
![](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/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2551d93b674b9f8bcd0e88454c99eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb96e0331eebe80ed1ff610faf531fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/1180cd27-53de-4a5a-a91b-f512b407ca67.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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8 . 如图,圆柱
的底面圆半径为
,
为经过圆柱轴
的截面,点
在
上且
,
为
上任意一点.
![](https://img.xkw.com/dksih/QBM/2020/1/5/2370732458287104/2370789363023872/STEM/33cb5b6fb0bf4329b86fe75c2ed9d704.png?resizew=189)
(1)求证:
;
(2)若直线
与面
所成的角为
,求圆柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d77b3ca5de6584c7d4ca5fdafbb8d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50081ec1e64530e465104a2f2bbb3f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2020/1/5/2370732458287104/2370789363023872/STEM/33cb5b6fb0bf4329b86fe75c2ed9d704.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2180eeee8897d83729ccf0916456b726.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
您最近一年使用:0次
9 . 如图:四面体
的底面
是直角三角形,
,
,
,
平面
,
,
是
上的动点(不包括端点).
![](https://img.xkw.com/dksih/QBM/2019/11/11/2331835834687488/2331865865527296/STEM/d0e9f5a07f8140ada39c211c9225cab2.png?resizew=189)
(1)求证:
与
不垂直;
(2)当
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.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/441a92c002129b752085f041139e2e2c.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/2019/11/11/2331835834687488/2331865865527296/STEM/d0e9f5a07f8140ada39c211c9225cab2.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c05986ad5fa244bc1aedf7b5d216544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91a39d25ede9815a42c52a08b57f7c3.png)
您最近一年使用:0次
2019-11-11更新
|
446次组卷
|
3卷引用:2019年上海市建平中学高三三模数学试题
10 . 《九章算术》中,将底面为长方形且有一条侧棱与地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,首届中国国际进口博览会的某展馆棚顶一角的钢结构可以抽象为空间图形阳马,如图所示,在阳马
中,
底面
.
(1)已知
,斜梁
与底面
所成角为
,求立柱
的长;(精确到
)
(2)求证:四面体
为鳖臑.
![](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)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99571b26b832c7522ed80a7bc884eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c12e76fbd84eeec721386bd3b04cc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6816ac6ff3f3df456865d0135802d5.png)
(2)求证:四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96e070966ddc1d779fcfae475715936.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/a1d9b5b3-437e-45db-863d-d68fd263f1a0.png?resizew=207)
您最近一年使用:0次
2018-12-30更新
|
278次组卷
|
3卷引用:2019年上海市长宁(嘉定)区高三上学期期末质量检测(一模)数学试题