名校
解题方法
1 . 如图正方体
,
、
分别为
、
的中点,
是线段
上的动点(包括端点),下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/7f90d2d7-1ad0-4f60-ae84-292f0654ecde.png?resizew=212)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/7f90d2d7-1ad0-4f60-ae84-292f0654ecde.png?resizew=212)
A.对于任意![]() ![]() ![]() |
B.存在![]() ![]() ![]() |
C.存在![]() ![]() ![]() |
D.对于任意![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
2 . 三棱柱
的棱长都为2,D和E分别是
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/3afad949-d5f9-4337-a9f2-0d0da9a7a9d2.png?resizew=217)
(1)求证:直线
平面
;
(2)若
,点B到平面
的距离为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/3afad949-d5f9-4337-a9f2-0d0da9a7a9d2.png?resizew=217)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a57dfb78e8579cc68dbfca90f80a1c5.png)
您最近一年使用:0次
2023-04-21更新
|
2327次组卷
|
6卷引用:浙江省杭州第二中学等四校联盟2022-2023学年高一下学期期中联考数学试题
浙江省杭州第二中学等四校联盟2022-2023学年高一下学期期中联考数学试题(已下线)【2023】【高一下】【期中考】【330】【高中数学】(已下线)13.3 空间图形的表面积和体积(分层练习)第八章 立体几何初步(单元测试)-【同步题型讲义】(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(1)辽宁省抚顺市六校协作体2022-2023学年高一下学期期末考试数学试题
名校
解题方法
3 . 如图①所示,已知正三角形
与正方形
,将
沿
翻折至
所在的位置,连接
,
,得到如图②所示的四棱锥.已知
,
,
为
上一点,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/0d855ffa-0ab1-4d06-900f-8e584e0b373d.png?resizew=259)
(1)求证:
平面
;
(2)在线段
上是否存在一点
,使得
平面
.若存在,指出点
的位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3736237f7bc84fc30f0bd75d5bba9242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad895b1c422b40c35be89c8bef22e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2c39a3d57d2de07a21550fe138ff77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6117f4a30d930911d33698444e8527f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bd11c1ac25b222f9613428412090a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/0d855ffa-0ab1-4d06-900f-8e584e0b373d.png?resizew=259)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eef01d240d3674e0113d1064569bce.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc063cdcf722f07a1aa57be04edd416d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d987bcf7114c002843702100444da017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea3cebae1762106ecd2a4fd56d07763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2023-04-19更新
|
573次组卷
|
4卷引用:浙江省宁波市北仑中学2022-2023学年高一下学期期中数学试题
浙江省宁波市北仑中学2022-2023学年高一下学期期中数学试题(已下线)立体几何专题:立体几何探索性问题的8种考法(已下线)13.2 基本图形位置关系(分层练习)黑龙江省齐齐哈尔市第八中学校2022-2023学年高一下学期期末数学试题
名校
解题方法
4 . 如图所示,在四棱锥
中,四边形ABCD是梯形,
,
,E是PD的中点.
平面PAB;
(2)若M是线段CE上一动点,则线段AD上是否存在点
,使
平面PAB?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e306e30d3159e4a68435c3fcfc8da693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
(2)若M是线段CE上一动点,则线段AD上是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
您最近一年使用:0次
2023-09-09更新
|
793次组卷
|
5卷引用:浙江省嘉兴八校联盟2021-2022学年高一下学期期中联考数学试题
浙江省嘉兴八校联盟2021-2022学年高一下学期期中联考数学试题福建省福州屏东中学2023-2024学年高一下学期期中考试数学试卷(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)(已下线)8.5.3 平面与平面平行【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)6.4 .2 平面与平面平行-同步精品课堂(北师大版2019必修第二册)
名校
解题方法
5 . 如图,在棱长为2的正方体
中,P,Q分别是棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/adfe99d3-5f97-4225-b6bc-09af8ec54f10.png?resizew=147)
(1)若
为棱
上靠近
点的四等分点,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
平面PQC;
(2)若平面PQC与直线
交于
点,求平面PRQC将正方体分割成的上、下两部分的体积之比.(不必说明画法与理由).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/adfe99d3-5f97-4225-b6bc-09af8ec54f10.png?resizew=147)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
(2)若平面PQC与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在三棱柱
中,若G,H分别是线段AC,DF的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
;
(2)在线段CD上是否存在一点
,使得平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
平面BCF,若存在,指出
的具体位置并证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0147945bdf3db4bf5e40be746ef2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)在线段CD上是否存在一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2c1789c5361169483df2924acd7321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2023-04-13更新
|
3160次组卷
|
9卷引用:浙江省宁波市三锋教研联盟2022-2023学年高一下学期期中联考数学试题
浙江省宁波市三锋教研联盟2022-2023学年高一下学期期中联考数学试题(已下线)立体几何专题:立体几何探索性问题的8种考法(已下线)13.2.4 平面与平面的位置关系 (1)河北定州中学2022-2023学年高一下学期5月月考数学试题江西省宜春市第十中学2024届高二上学期开学检测数学试题新疆阿克苏市实验中学2022-2023学年高一下学期第三次月考数学试题(已下线)8.5.3 平面与平面平行【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)11.3.3平面与平面平行-同步精品课堂(人教B版2019必修第四册)(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
7 . 在矩形
中,AB=4,AD=2.点
分别在
上,且AE=2,CF=1.沿
将四边形
翻折至四边形
,点
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/4115fbbd-04cb-4551-9270-cb6e465c5275.png?resizew=396)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ba89e83329983cfadbfcdda151aaa3.png)
平面
;
(2)求异面直线
与
所成的角;
(3)在翻折的过程中,设二面角
的平面角为
,求
的最大值.
![](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/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946c16d99496d31ce4d87301a4793393.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c76e6c67644b8bad9bfe11c7ec3081d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7829855159327b2a87c3a424b3f7134a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/4115fbbd-04cb-4551-9270-cb6e465c5275.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ba89e83329983cfadbfcdda151aaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b12cffc313a181f666e3fc8e66b6f59.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
(3)在翻折的过程中,设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b43ff5a9a70210b4017c4c38b4258c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
您最近一年使用:0次
名校
解题方法
8 . 在边长为2的正方体
中,点M是该正方体表面及其内部的一动点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
平面
,则动点M的轨迹所形成区域的面积是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57132b0bd38c035fec010ee3be1bc8fe.png)
您最近一年使用:0次
2023-05-09更新
|
1523次组卷
|
12卷引用:浙江省杭州市八校联盟2020-2021学年高一下学期期中联考数学试题
浙江省杭州市八校联盟2020-2021学年高一下学期期中联考数学试题(已下线)【新东方】高中数学20210527-032【2021】【高一下】江西省南昌市进贤第一中学2020-2021学年高二下学期期中考试数学(理)试题广东省珠海市斗门第一中学2021-2022学年高一下学期期中数学试题北京市门头沟区2021届高三数学一模试题(已下线)专题06空间位置关系的判断与证明湖北省武汉市第六中学2022-2023学年高一下学期第六次月考数学试题宁夏贺兰县第一中学2022-2023年高一下学期数学期末复习试题(四)(已下线)第七章 立体几何与空间向量 第三节?第二课时直线,平面平行的判定与性质(A素养养成卷)(已下线)重难点突破04 立体几何中的轨迹问题(六大题型)山东省菏泽外国语学校2023-2024学年高一下学期第二次月考数学试题(已下线)核心考点5 立体几何中的位置关系 B提升卷 (高一期末考试必考的10大核心考点)
21-22高一下·浙江·期中
9 . 已知三棱锥
中,△ABC,△ACD都是等边三角形,
,E,F分别为棱AB,棱BD的中点,G是△BCE的重心.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/4c768d18-52ee-428a-958c-36eeb689cbf2.png?resizew=196)
(1)求异面直线CE与BD所成角的余弦值;
(2)求证:FG
平面ADC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b94651d11df3a469d7ac72e6ac74c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/4c768d18-52ee-428a-958c-36eeb689cbf2.png?resizew=196)
(1)求异面直线CE与BD所成角的余弦值;
(2)求证:FG
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
您最近一年使用:0次
20-21高一下·浙江·期末
名校
解题方法
10 . 如图,正方体
的棱长为1,
,
分别是棱
,
的中点,过
的平面与棱
,
分别交于点
,
.设
,
.以下结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/f9be9874-ef25-4c3d-99ba-5b29157fffce.png?resizew=163)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.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/3aa7e162d36074987cecd874f946480d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/f9be9874-ef25-4c3d-99ba-5b29157fffce.png?resizew=163)
A.四边形![]() |
B.![]() ![]() |
C.四边形![]() ![]() ![]() |
D.四棱锥![]() |
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