名校
解题方法
1 . 如图所示,在四棱锥
中,底面ABCD为正方形,PA⊥底面ABCD,PA=AB=4.E,F,H分别是棱PB,BC,PD的中点,对于平面EFH截四棱锥
所得的截面多边形,有以下三个结论:
;
②截面是一个五边形;
③直线PC与截面所在平面EFH无公共点.
其中,所有正确结论的序号是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee05b3210c8964deef8ff771173d288.png)
②截面是一个五边形;
③直线PC与截面所在平面EFH无公共点.
其中,所有正确结论的序号是
您最近一年使用:0次
2022-06-02更新
|
853次组卷
|
3卷引用:北京市陈经纶中学2021-2022学年高一下学期期中诊断考试数学试题
北京市陈经纶中学2021-2022学年高一下学期期中诊断考试数学试题北京市陈经纶中学2023-2024学年高一下学期期中练习数学试卷(已下线)高一下期中真题精选(压轴60题专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
名校
解题方法
2 . 在棱长为2的正方体
中,点E、F分别是棱BC,
的中点,P是侧面四边形
内(不含边界)一点,若
平面AEF,则线段
长度的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e2d69b11402d9d6cbb06e057778a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
您最近一年使用:0次
2022-05-12更新
|
3680次组卷
|
17卷引用:北京市景山中学2021-2022学年高一下学期期中考试数学试题
北京市景山中学2021-2022学年高一下学期期中考试数学试题湖南省邵阳市第二中学2021-2022学年高一下学期期中数学试题湖北省华中师范大学第一附属中学2021-2022学年高一下学期5月月考数学试题新疆石河子第一中学2021-2022学年高一下学期5月月考数学试题(已下线)8.5.3 平面与平面平行 (精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)第八章《立体几何初步》单元达标高分突破必刷卷(培优版)-《考点·题型·技巧》(已下线)专题强化三 直线、平面的平行和垂直问题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)湖北省武汉市部分中学2021-2022学年高一下学期5月联考数学试题辽宁省大连市第八中学2021-2022学年高一下学期6月月考数学试题吉林省延边朝鲜族自治州延吉市延边第二中学2022-2023学年高一下学期期中数学试题专题11空间中直线、平面的平行与垂直关系(选择填空题)黑龙江省哈尔滨市德强高级中学2021-2022学年高一下学期期中数学试题湖南省邵阳市第二中学2023-2024学年高一下学期4月期中数学试题陕西省西安中学2022届高三下学期三模文科数学试题(已下线)考点7-1 平行垂直与动点(文理)(已下线)点线面之间的位置关系(已下线)第2题 空间中截面最值问题(压轴小题)
3 . 正方体
中,
是的
中点,
是线段
上的一点. 给出下列命题:
![](https://img.xkw.com/dksih/QBM/2021/8/13/2785290337861632/2786879779913728/STEM/2e40dda5-15df-439c-9473-34d7e5d2bbd6.png?resizew=233)
① 平面
中一定存在直线与平面
垂直;
② 平面
中一定存在直线与平面
平行;
③ 平面
与平面
所成的锐二面角不小于
;
④ 当点
从点
移动到点E时,点
到平面
的距离逐渐减小.其中,所有真命题的序号是___________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://img.xkw.com/dksih/QBM/2021/8/13/2785290337861632/2786879779913728/STEM/2e40dda5-15df-439c-9473-34d7e5d2bbd6.png?resizew=233)
① 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
② 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
③ 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
④ 当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
您最近一年使用:0次
2021-08-15更新
|
730次组卷
|
3卷引用:北京市延庆区2020-2021学年高一下学期期末考试数学试题
名校
解题方法
4 . 已知四棱锥
的底面为直角梯形,
平面
,且
,
是棱
上的动点.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759915792539648/2767376669040640/STEM/4d920b52ff4b43338e777fb055e873e7.png?resizew=202)
(1)求证:平面
平面
;
(2)若
平面
,求
的值;
(3)当
是
中点时,设平面
与棱
交于点
,求截面
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84250c37e63bebcc57bb628bf5b1b838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda1a7eeb84ee2f5f723c78de0867aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759915792539648/2767376669040640/STEM/4d920b52ff4b43338e777fb055e873e7.png?resizew=202)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36222db36e348661eb5f616820e4e60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59a8e73d86982a4882510a179b0efb0.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ab4fdfc612c9fa2dd8ae24904192d8.png)
您最近一年使用:0次
2021-07-19更新
|
1539次组卷
|
3卷引用:北京师范大学附属中学2020-2021学年高一下学期期末数学试题
北京师范大学附属中学2020-2021学年高一下学期期末数学试题(已下线)专题8.14 空间直线、平面的垂直(二)(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)福建省宁德第一中学2022-2023学年高一下学期5月月考数学试题
名校
5 . 如图,在棱长为1的正方体
中,点
分别是棱
的中点,
是侧面
内一点,若
平面
,则下列说法正确的是__________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/164a9983-3216-4792-a001-7018751bce3f.png?resizew=163)
①线段
的最大值是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e3e58e5d7cdd7c90360e14a9d0c214.png)
③
与
一定异面
④三棱锥
的体积为定值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334bd1a151c0a42ca813cb6b839ce45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e2d69b11402d9d6cbb06e057778a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/164a9983-3216-4792-a001-7018751bce3f.png?resizew=163)
①线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e3e58e5d7cdd7c90360e14a9d0c214.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d75d48f7a1612807bdd878c774394b.png)
您最近一年使用:0次
2021-07-19更新
|
1814次组卷
|
6卷引用:北京师范大学附属中学2020-2021学年高一下学期期末数学试题
6 . 如图所示,在正方体
中,点
在棱
上,且
,点
、
、
分别是棱
、
、
的中点,
为线段
上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/6cdf8094-b71d-4477-865e-03ffabb084f5.png?resizew=148)
(1)若平面
交平面
于直线
,求证:
;
(2)若直线
平面
,
①求三棱锥
的表面积;
②试作出平面
与正方体
各个面的交线,并写出作图步骤,保留作图痕迹设平面
与棱
交于点
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f01d1dd10776b00e9df008f03f2608c.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/6cdf8094-b71d-4477-865e-03ffabb084f5.png?resizew=148)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a447dc58e10adb7c8014071651e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ba669c69462fbbff2ef12ea9015fc8.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a447dc58e10adb7c8014071651e7c9.png)
①求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b03980f99fa0f339388e564466e8b94.png)
②试作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf62b9fe96ad0b0f58c8b3ba3075ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf62b9fe96ad0b0f58c8b3ba3075ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4a7ba7546acc68f9cff46f1c53557f.png)
您最近一年使用:0次
2020-11-06更新
|
1995次组卷
|
6卷引用:北京市中国人民大学附属中学2019-2020学年高一下学期数学期末练习试题
北京市中国人民大学附属中学2019-2020学年高一下学期数学期末练习试题北京市第八十中学2021-2022学年高一下学期期中考试数学试题(已下线)专题05 立体几何初步(重点)-2020-2021学年高一数学下学期期末专项复习(北师大版2019必修第二册)(已下线)专题06 立体几何初步(难点)-2020-2021学年高一数学下学期期末专项复习(北师大版2019必修第二册)江苏省镇江第一中学2021-2022学年高一下学期6月月考数学试题(已下线)高一下学期期末真题精选(压轴60题20个考点专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
名校
解题方法
7 . 如图1,在等腰梯形
中,
,
,
,
,E、F分别为腰
、
的中点.将四边形
沿
折起,使平面
平面
,如图2,H,M别线段
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/9066276c-44d7-477f-a965-e155543e93ed.png?resizew=413)
(1)求证:
平面
;
(2)请在图2所给的点中找出两个点,使得这两点所在直线与平面
垂直,并给出证明:
(3)若N为线段
中点,在直线
上是否存在点Q,使得
面
?如果存在,求出线段
的长度,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.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/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744c636a21ef089c9239eeafff4b83ea.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/9066276c-44d7-477f-a965-e155543e93ed.png?resizew=413)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a984e08781547575be9680e8c61bb21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d4b05a1402beb3f13d4ce7d22089b9.png)
(2)请在图2所给的点中找出两个点,使得这两点所在直线与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769f81c1b5a405e2e7eb78f199f9e6e.png)
(3)若N为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d42170c7d4249f6b390823606c18c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a158113467436c24c6db00f058cf91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769f81c1b5a405e2e7eb78f199f9e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
您最近一年使用:0次
2020-11-02更新
|
1357次组卷
|
4卷引用:北京市密云区2019-2020学年高一下学期数学期末试题
8 . 如图,在多面体
中,平面
平面
,四边形
为正方形,四边形
为梯形,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0911cb29-c63c-459a-a253-5688566270ed.png?resizew=190)
(Ⅰ)求证:
平面
;
(Ⅱ)求证:
平面
;
(Ⅲ)在线段
上是否存在点
,使得
平面
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0254c51c4e3e5ca7190cb4cd97defbb5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/0911cb29-c63c-459a-a253-5688566270ed.png?resizew=190)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5edfe97aeab0cf16b40fa9d2e15f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(Ⅲ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75445760eb6944d4c380707bc83ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf38d5288cbde3baf715bd0ca6c4dadb.png)
您最近一年使用:0次
2019-07-08更新
|
2923次组卷
|
5卷引用:北京市朝阳区2018-2019学年高一下学期期末数学试题
9 . 如图所示,在长方体
中,
,点E是棱
上的一个动点,若平面
交棱
于点
,给出下列命题:.
的体积恒为定值;
②存在点
,使得
平面
;
③存在唯一的点
,使得截面四边形
的周长取得最小值;
④存在无数个点
,在棱
上均有相应的点
,使得
平面
,也存在无数个点
,对棱
上任意的点
, 直线
与平面
均相交.
其中真命题的是____________ .(填出所有正确答案的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372aca10d328d3ba60918761ec68c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3952eed71873e335de396daa539c34.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f708871a163c330bd4462ca18de96c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f611501942b181e66502278e9882e1.png)
③存在唯一的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6069dc466eec75bbeb3d5c9b51cb3a70.png)
④存在无数个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b509e51d8882449e28f181f19a36fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bed7c849fe4195db0cf9e13766f4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb11667abcb2759f301391b9850352be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bed7c849fe4195db0cf9e13766f4d1.png)
其中真命题的是
您最近一年使用:0次
2019-04-25更新
|
1478次组卷
|
3卷引用:【区级联考】北京市海淀区2018-2019学年高一下学期期中考试数学试题
【区级联考】北京市海淀区2018-2019学年高一下学期期中考试数学试题北京市中关村中学2021-2022学年高一六月调研数学试题(已下线)8.6.1直线与直线垂直+8.6.2直线与平面垂直——课后作业(基础版)
10 . 如图,菱形
的边长为
,
,
,将菱形
沿对角线
折起,得到三棱锥
,点
是棱
的中点,
.
![](https://img.xkw.com/dksih/QBM/2018/6/25/1975123304800256/null/STEM/2f79d6cb40b6435bbedbe04f0d268880.png?resizew=359)
(
)求证:
平面
.
(
)求证:平面
平面
.
(
)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14b9e6dfaf58b8159e4f2d3b9bd6645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4c1ba8858e3a21de22315e5a0b1353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f93febecbed16fb12a40424cc5be74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3926b75121355e46986708f3cb8cac73.png)
![](https://img.xkw.com/dksih/QBM/2018/6/25/1975123304800256/null/STEM/2f79d6cb40b6435bbedbe04f0d268880.png?resizew=359)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce1ac49efbb1ef090f2cec1360ca55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c6ee63b22008f64730404a63967d11.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99bfa2ca4e398c8ab0f97f47add3754f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657ffb23fab8129beb441b0c681e3dab.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c392e7a5af629bd60c1f91fbb8d5a68.png)
您最近一年使用:0次