名校
解题方法
1 . 如图,在四面体PABC中,
,
,点D,E,F,G分别是棱AP,AC,BC,PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/20/8b75caeb-7aa0-482d-a804-79fe253e212b.png?resizew=156)
(1)求证:
平面BCP;
(2)求证:四边形DEFG为矩形;
(3)是否存在点Q,到四面体PABC六条棱的中点的距离相等?若存在,写出点Q的位置(不需要论证).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e4b16c2c6c9bd089da78122e9d2511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/20/8b75caeb-7aa0-482d-a804-79fe253e212b.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75aea24647cd4d0b4b9aa513bf5457b0.png)
(2)求证:四边形DEFG为矩形;
(3)是否存在点Q,到四面体PABC六条棱的中点的距离相等?若存在,写出点Q的位置(不需要论证).
您最近一年使用:0次
2 . 如图,在正方体
中,
是
的中点,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/13/b5a35b96-c5d1-4f74-8c1f-69c81ef0065f.png?resizew=198)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)若
,求:棱锥
体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/13/b5a35b96-c5d1-4f74-8c1f-69c81ef0065f.png?resizew=198)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cd14cd2875ed363428c3e8918b74a7.png)
您最近一年使用:0次
名校
解题方法
3 . 如图所示,在三棱锥
中,已知△BCD是正三角形,AB⊥平面BCD,AB=BC=2,E为BC的中点,F在棱AC上,且AF=3FC.
![](https://img.xkw.com/dksih/QBM/2022/5/28/2989384177262592/2992913813864448/STEM/4ef5aa63-3523-4ea1-9bf1-95d5593a990f.png?resizew=268)
(1)求证:AC⊥DE;
(2)若M为BD的中点,问AC上是否存在一点N,使
平面DEF?若存在,说明点N的位置;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://img.xkw.com/dksih/QBM/2022/5/28/2989384177262592/2992913813864448/STEM/4ef5aa63-3523-4ea1-9bf1-95d5593a990f.png?resizew=268)
(1)求证:AC⊥DE;
(2)若M为BD的中点,问AC上是否存在一点N,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在四棱锥
中,底面
是正方形,侧面
底面
,E为侧棱
上一点.
![](https://img.xkw.com/dksih/QBM/2022/5/20/2983604447739904/2992793877364736/STEM/9cd62997-5b4f-4361-8ef5-e881b5e05014.png?resizew=156)
(1)求证:
平面
;
(2)求证:
;
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2022/5/20/2983604447739904/2992793877364736/STEM/9cd62997-5b4f-4361-8ef5-e881b5e05014.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6785c7c85a503531649f9c9b4cbfcf04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dac702fe64edf1bc265da4b98cf2a0.png)
您最近一年使用:0次
2022-06-02更新
|
880次组卷
|
3卷引用:北京市黄冈中学北京朝阳学校2021-2022学年高一下学期期中考试数学试题
北京市黄冈中学北京朝阳学校2021-2022学年高一下学期期中考试数学试题(已下线)核心考点08空间直线、平面的垂直-【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)山西省酒泉市酒泉师范学校(酒泉市实验中学)2023-2024学年高二上学期学业水平合格性考试模拟卷(一)数学试题
名校
解题方法
5 . 如图,在直角梯形
中,
,
,
.以直线
为轴,将直角梯形
旋转得到直角梯形
,使得平面
平面
,点
为线段
上一点,且
.
平面
;
(2)求证:
;
(3)若平面BCEF与直线AG相交于点H,试确定点H的位置,并求线段BH的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4299cca48ff6abfb252ef73b5e62317d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e9785a8ffb637c91757fe01d3c23a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e9785a8ffb637c91757fe01d3c23a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa52f8136b86703a61d0a524fb8596f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d888c0b616792a2c41ff180de99fbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbee06d305abf6692125513dc3757f9.png)
(3)若平面BCEF与直线AG相交于点H,试确定点H的位置,并求线段BH的长.
您最近一年使用:0次
2022-07-08更新
|
608次组卷
|
5卷引用:北京市昌平区2021-2022学年高一下学期期末质量抽测数学试题
北京市昌平区2021-2022学年高一下学期期末质量抽测数学试题(已下线)8.4.2 空间点、直线、平面之间的位置关系(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)江苏省南京航空航天大学附属高级中学2022-2023学年高一下学期6月月考数学试题(已下线)核心考点06空间点、直线、平面的位置关系-【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)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(1)-期期末真题分类汇编(北京专用)
解题方法
6 . 在直三棱柱
中,
,D、E、F分别为棱
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/13d77b45-67fb-41ea-9936-2df546a427f1.png?resizew=124)
(1)求证:
平面
;
(2)求证:
;
(3)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3788d69acba900ae9e013ef0a23bb347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d6885901907652b1653be2cef5f665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/13d77b45-67fb-41ea-9936-2df546a427f1.png?resizew=124)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bc51695e51aa8cd2f97d220c8f5340.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a7a3dc3f3a02f4400e22dec2f2fee23.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5034b24ff73d35c3f34e5c45daa0624d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05925f665156215b1e031ea6c190616a.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在三棱锥V-ABC中,平面VAC⊥平面ABC,△VAC,△ABC都是等腰直角三角形,AB=BC,AC=VC,M,N分别为VA,VB的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974166519259136/2979728830742528/STEM/087cedafd7b7487cabc568a16467ecf2.png?resizew=156)
(1)求证:AB//平面CMN;
(2)求证:AB⊥平面VBC.
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974166519259136/2979728830742528/STEM/087cedafd7b7487cabc568a16467ecf2.png?resizew=156)
(1)求证:AB//平面CMN;
(2)求证:AB⊥平面VBC.
您最近一年使用:0次
2022-05-15更新
|
837次组卷
|
4卷引用:北京市怀柔区2021-2022学年高二上学期期末数学试题
北京市怀柔区2021-2022学年高二上学期期末数学试题(已下线)专题20 立体几何中垂直问题的证明-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)江苏省常州市武进区礼嘉中学2021-2022学年高二下学期阶段测试数学试题四川省射洪中学校2022-2023学年高二上学期期中数学(文)试题
8 . 如图,在正方体
中,
是棱
上一点,且
.
三点的平面截正方体
所得截面
;
(2)证明:平面
与平面
相交,并指出它们的交线.
![](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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d541d01f33c3a65e7963e8b11da2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bace5a20a202a9bc3c1e8b1e10e7c1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59375dfae3a8ec264204cfe78caac97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-07-07更新
|
1552次组卷
|
9卷引用:北京市房山区2021—2022学年高一下学期期末学业水平调研数学试题
北京市房山区2021—2022学年高一下学期期末学业水平调研数学试题(已下线)8.4.1 平面(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)第25讲 平面的交线截面问题(已下线)核心考点06空间点、直线、平面的位置关系-【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)(已下线)第七章 立体几何与空间向量 第二节?空间点、直线、平面之间的位置关系 讲(已下线)第二章 立体几何中的计算 专题四 空间几何体截面问题 微点5 空间几何体截面问题综合训练【培优版】(已下线)8.4.2空间点、直线、平面之间的位置关系(第2课时)(已下线)专题17 空间点、直线、平面之间的关系-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(1)-期期末真题分类汇编(北京专用)
名校
9 . 如图,在棱长为
的正方体
中,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/7cbf8dc8-f6be-42ce-8e1b-47b3bfe3f968.png?resizew=176)
(1)求证:
平面
;
(2)求二面角
的大小;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/7cbf8dc8-f6be-42ce-8e1b-47b3bfe3f968.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f3750c0616ecc1d9dc8d905e26a9cc.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e729d9e7acf6f180c311622c251fd30.png)
您最近一年使用:0次
2022-05-11更新
|
1297次组卷
|
2卷引用:北京市昌平区2022届高三二模数学试题
名校
解题方法
10 . 如图,已知在四棱锥
中,底面
是平行四边形,
为
的中点,在
上任取一点
,过
和
作平面
交平面
于
.
![](https://img.xkw.com/dksih/QBM/2022/6/8/2996963430260736/2998264787140608/STEM/46c2e4c38db54249a85c697061079e9d.png?resizew=183)
(1)求证:
平面
;
(2)求证:
平面
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1b63ff147840a325bfd8653136b05d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838132d6d6d5177def1270bddeee3d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://img.xkw.com/dksih/QBM/2022/6/8/2996963430260736/2998264787140608/STEM/46c2e4c38db54249a85c697061079e9d.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d8677ae5ca7acf874d93789425d172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6ef7306c5965dbe4d0259102d6b74c.png)
您最近一年使用:0次