名校
解题方法
1 . 如图,在四棱锥
中,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1573ea134172e6f4aab6ebd047f29757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
为棱
的中点,平面
与棱
相交于点
,且
,再从下列两个条件中选择一个作为已知.
条件①:
;条件②:
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
;
(2)求点
到平面
的距离;
(3)已知点
在棱
上,直线
与平面
所成角的正弦值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1573ea134172e6f4aab6ebd047f29757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0be0f7a9612bf6b40139609e3d0aac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7901ce9a29748df90f3996d24df188f.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2c4b7601274731a0f8140c99762501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15a004f7d47ed595f063e60075223a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d70fb53a3bc46be3e6365f5ed26496.png)
(3)已知点
![](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/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d70fb53a3bc46be3e6365f5ed26496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0519ba613bf121a2c1bc28c948266d74.png)
您最近一年使用:0次
2024-01-22更新
|
402次组卷
|
3卷引用:江西省宜春市上高二中2024届高三下学期5月月考数学试卷
2 . 如图,在多面体
中,四边形
和四边形
是全等的直角梯形,且这两个梯形所在的平面相互垂直,其中
,
.
(1)证明:
平面
;
(2)若
,求点F到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef094b976004572464bedaddc76ee6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c1053471b8f2f717dd53c05fd58d7f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/e630f7d3-c8d9-4b30-9f99-515e7378fb85.png?resizew=173)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
3 . 已知四棱锥
如图所示,平面
平面
,四边形
为菱形,
为等边三角形,直线
与平面
所成角的正切值为1.
;
(2)若点
是线段AD上靠近
的四等分点,
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5830322dd2824ed012a68f1a2bd9c742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5578cd49feb7c846f087b041371c3875.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5da631296d53a08d56fb5f9bec2376c.png)
您最近一年使用:0次
2024-01-02更新
|
923次组卷
|
6卷引用:江西省上饶市玉山县第二中学2024届高三上学期12月月考数学试题
江西省上饶市玉山县第二中学2024届高三上学期12月月考数学试题(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(十一)(已下线)第16讲 拓展一:立体几何中空间角的问题和点到平面距离问题-【帮课堂】(人教A版2019必修第二册)(已下线)专题8.9 空间角与空间距离大题专项训练-举一反三系列(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)(已下线)11.4.2平面与平面垂直-同步精品课堂(人教B版2019必修第四册)
解题方法
4 . 已知三棱锥
中,
,
平面
,
,则
到平面
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca6c58cd96a02af69710fe1cd2c6d57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317430d5a2b61d9a2a88b73e7d7ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183ec02812ee8cda06c714eb3cee0ad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2024-01-07更新
|
149次组卷
|
2卷引用:江西省上饶市广丰贞白中学2024届高三上学期1月考试数学试题
名校
解题方法
5 . 如图,在长方体
中,
,
和
交于点E,F为AB的中点.
平面
;
(2)已知
与平面
所成角为
,求点A到平面CEF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745717601cd14b46c2298919b41b502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
您最近一年使用:0次
2024-01-05更新
|
456次组卷
|
5卷引用:江西省景德镇市景德镇一中2024届高三上学期1月考试数学试题
江西省景德镇市景德镇一中2024届高三上学期1月考试数学试题宁夏石嘴山市平罗中学2024届高三上学期第四次月考数学(文)试题(已下线)专题8.9 空间角与空间距离大题专项训练-举一反三系列(已下线)第八章 立体几何初步(二)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)(已下线)重难点专题15 空间中的五种距离问题-【帮课堂】(苏教版2019必修第二册)
6 . 如图,在四棱锥
中,底面是边长为2的菱形,
,
平面
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/97d598db-8bba-4aff-a185-4cf37552979f.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a619db37ee421ae3f52e51f5d479b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/97d598db-8bba-4aff-a185-4cf37552979f.png?resizew=180)
A.![]() | B.![]() |
C.![]() | D.点![]() ![]() |
您最近一年使用:0次
2023-12-21更新
|
193次组卷
|
2卷引用:江西省上饶艺术学校2023--2024学年高二上学期1月月考数学试题
名校
解题方法
7 . 如图在四棱锥
中,底面
是正方形,侧棱
底面
,
,
是
中点,作
交
于点
.
(1)求证:
平面
;
(2)求证:PB
平面
;
(3)求
点到平面
的距离.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d4d36ae30487030b827ce9413b9f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4a6a1e70241d600bc6c104313eac61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/0db22f59-24d4-4d50-95d1-ec5bb95a7512.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466fabcaac59132fea648ff35342ec9d.png)
(2)求证:PB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebce46aeb97373353179e5669365fa4a.png)
您最近一年使用:0次
2023-12-15更新
|
444次组卷
|
2卷引用:江西省上饶市上饶中学2024届高三上学期12月月考数学试题
名校
解题方法
8 . 如图,在三棱柱
中,侧面
是边长为
的正方形,
为矩形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/51c6946c-8df2-4aed-b56f-f0f204c9e6f7.png?resizew=139)
(1)求证:
平面ABC;
(2)求平面
与平面
所成角的正弦值;
(3)求点C到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9fb806bf3862d351dc4e4ffa3a2283.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/21/51c6946c-8df2-4aed-b56f-f0f204c9e6f7.png?resizew=139)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
(3)求点C到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
您最近一年使用:0次
2023-11-22更新
|
599次组卷
|
6卷引用:江西省宜春市丰城市东煌学校2023-2024学年高二上学期12月月考数学试题
名校
解题方法
9 . 已知正方形
的边长为2,
为等边三角形(如图1所示).沿着
折起,点
折起到点
的位置,使得侧面
底面
.
是棱
的中点(如图2所示).
(1)求证:
;
(2)求点
与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef328d61bcf3cece520c35a2ce449ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee6765a83140d745a6de4c85d9b6b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.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/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/c4e761e3-e1ef-41fe-a956-695d6e0d6309.png?resizew=336)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/789c9c79846abc6ba99cf3e575cdae6f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03203dd5ac79dd8c6707e4340773359.png)
您最近一年使用:0次
2023-10-19更新
|
432次组卷
|
4卷引用:江西省宜春市上高二中2023-2024学年高二上学期第三次月考数学试题
江西省宜春市上高二中2023-2024学年高二上学期第三次月考数学试题江西省新余市实验中学2023-2024学年高二上学期12月月考试数学试题四川省成都市教科院附中2023-2024学年高三上学期10月月考数学(文)试题(已下线)考点9 垂直的判定与性质 2024届高考数学考点总动员【练】