名校
解题方法
1 . 已知在四棱锥
中,底面ABCD为边长为4的正方形,E为PA的中点,过E与底面ABCD平行的平面
与棱PC,PD分别交于点G,F,点M在线段AE上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/df11ec05-740a-4714-b076-0459d1d0a59a.png?resizew=181)
(1)求证:
平面CFM;
(2)若
平面ABCD,且
,求点G到平面CFM的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809669f31487e232adf580fa586d759b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/df11ec05-740a-4714-b076-0459d1d0a59a.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5fba3cf6bbe668c2d49186d746b4a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19f0fcacac715a1200770516d1e4a67.png)
您最近一年使用:0次
2023-04-18更新
|
396次组卷
|
2卷引用:江西省抚州市金溪县第一中学2023届高三下学期4月考试数学(文)试题
名校
解题方法
2 . 如图,在直角梯形ABCD中,AB∥CD,AB⊥AD,且AB=AD=
=1.现以AD为一边向梯形外作正方形ADEF,然后沿边AD将正方形ADEF折叠,使ED⊥DC,M为ED的中点,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/5442594c-e0b5-4c3a-8f91-2fe81292cb48.png?resizew=414)
(1)求证:BC⊥平面BDE;
(2)求点D到平面BEC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b840be5852709e18ea985954545e78d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/5442594c-e0b5-4c3a-8f91-2fe81292cb48.png?resizew=414)
(1)求证:BC⊥平面BDE;
(2)求点D到平面BEC的距离.
您最近一年使用:0次
2022-11-12更新
|
451次组卷
|
3卷引用:江西省临川第一中学2022-2023学年高二上学期11月质量监测数学试题
江西省临川第一中学2022-2023学年高二上学期11月质量监测数学试题广东省肇庆市四会中学、广信中学2022-2023学年高二上学期第一次教学质量联考数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精讲)(1)-【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)
名校
解题方法
3 . 如图,在三棱锥
中,
平面ABC,
,
,
,则点A到平面PBC的距离为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91708c4508371f08556e76e31c7cb9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
A.![]() | B.![]() | C.3 | D.![]() |
您最近一年使用:0次
2022-07-10更新
|
1727次组卷
|
9卷引用:江西省临川第一中学2022-2023学年高二上学期10月质量监测数学试题
江西省临川第一中学2022-2023学年高二上学期10月质量监测数学试题湖北省恩施州咸丰春晖学校2022-2023学年高二上学期9月月考数学试题河南省豫东名校2021-2022学年高一下学期期末数学试题湖北省华中师范大学第一附属中学2021-2022学年高一下学期期末数学试题(已下线)专题强化训练四 直线与平面所成的角、二面角的平面角的常见解法(1)-《考点·题型·技巧》(已下线)专题10 空间角与空间距离的综合(1)-期中期末考点大串讲(已下线)期末专题08 立体几何小题综合-【备战期末必刷真题】(已下线)第四节?直线,平面垂直的判定与性质(讲)(已下线)第11章:立体几何初步章末重点题型复习(2)-【帮课堂】(人教B版2019必修第四册)
名校
解题方法
4 . 如图,在四棱锥P-ABCD中,ABCD为平行四边形,
,
平面ABCD,且
,E是PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/e5166a03-af3c-4ae6-a89b-06c4c2c9f03d.png?resizew=178)
(1)证明:
平面AEC;
(2)求点D到平面AEC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e624e6ee68b796f70f9d35e78a8aed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/e5166a03-af3c-4ae6-a89b-06c4c2c9f03d.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
(2)求点D到平面AEC的距离.
您最近一年使用:0次
2022-05-02更新
|
305次组卷
|
2卷引用:江西省金溪县第一中学2022-2023学年高二上学期第一次月考数学试题
名校
解题方法
5 . 如图,四边形
为正方形,
,
,且
,
,延长
相交于点
,连接
,
平面
.
![](https://img.xkw.com/dksih/QBM/2021/9/28/2817907379585024/2821526296436736/STEM/3aabd719b0e8420ca9107259815edb09.png?resizew=261)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae4c5cfe83c44c72a2d40695d18b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64f0bc01c1dbf0b4b87763141d8059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b021a72721e6ac70349104f8bf4b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012434c2c590eb70714d7c24fd63eaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c81e1db197be2e4b396000fbaa3129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://img.xkw.com/dksih/QBM/2021/9/28/2817907379585024/2821526296436736/STEM/3aabd719b0e8420ca9107259815edb09.png?resizew=261)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb8697622fb9d281cf44feb4adaf14a.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,在直三棱柱
中,
,点M为
的中点,点N为
上一动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/0f9e8ed0-0a53-4e8f-8ef2-c82120090898.png?resizew=190)
(1)是否存在点N,使得线段
平面
?若存在,指出点N的位置,若不存在,请说明理由;
(2)若点N为
的中点,且
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528cf687f3727fa0f827a3d90c9041cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/0f9e8ed0-0a53-4e8f-8ef2-c82120090898.png?resizew=190)
(1)是否存在点N,使得线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)若点N为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bd173466089f8e523dc02808239daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f41038b29426e9e592cd50c1b71e7e.png)
您最近一年使用:0次
2021-09-24更新
|
614次组卷
|
3卷引用:江西省抚州市临川第一中学2021-2022高二12月月考数学(文)试题
江西省抚州市临川第一中学2021-2022高二12月月考数学(文)试题北师大版 必修2 过关斩将 第一章 立体几何初步 本章复习提升(已下线)第二章 立体几何中的计算 专题三 空间体积的计算 微点5 空间图形体积的计算方法【培优版】
名校
解题方法
7 . 如图,在斜三棱柱
中,
是
的中点,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d0965977-06d8-472a-8070-c2e95c7690b8.png?resizew=224)
(1)求证:
⊥平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e89a358226b4be8786077a60555c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ea8821d44ee1f9332096263e7508e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d0965977-06d8-472a-8070-c2e95c7690b8.png?resizew=224)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
您最近一年使用:0次
名校
解题方法
8 . 如图所示,正方体
的棱长为
,
分别为
的中点.则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/3b61fe73-c13a-42e7-b84b-c18581a360c8.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c013fe68d73441990aa11da1737c4805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0eeef2ce12bb9df07327a650de0ba2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/3b61fe73-c13a-42e7-b84b-c18581a360c8.png?resizew=185)
A.直线![]() | B.直线![]() |
C.平面AEF截正方体所得的截面面积为18 | D.点![]() ![]() |
您最近一年使用:0次
2021-07-26更新
|
268次组卷
|
2卷引用:江西省临川一中暨临川一中实验学校2022-2023学年高二4月月考数学试题
名校
解题方法
9 . 在四棱锥
中,底面
是矩形,平面
平面
,
,
是
的中点.
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505229941760000/2506474520821760/STEM/e6d1788f-5244-46e0-b35b-3fc555be0d06.png)
(1)求证:
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4cab41e3c3e1b04f0cff21aca315238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505229941760000/2506474520821760/STEM/e6d1788f-5244-46e0-b35b-3fc555be0d06.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2919a92ec8fdae2a7b8511fff31fa65.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea051187d473c953b3d81a6ebe4d21f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f0106a1329dfce39bb51ae7c9c74ff.png)
您最近一年使用:0次
2020-07-15更新
|
219次组卷
|
4卷引用:江西省抚州市南城一中2020--2021学年高二4月月考数学(理)试题
10 . 在棱长为1的正方体
中,
分别为棱
、
的中点,
为棱
上的一点,且
,则点
到平面
的距离为( )
![](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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380c0e6bb85f13a03c30e6f3831660fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次