1 . 如图,将边长为2的正方形ABCD沿对角线BD折叠,使得平面ABD⊥平面CBD,AE⊥平面ABD,且
.
(2)求点C到平面BED的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c6c83ab4abc895ac36ab888a55be6.png)
(2)求点C到平面BED的距离.
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2023-05-25更新
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1102次组卷
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7卷引用:第10章 空间直线与平面(单元提升卷)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
(已下线)第10章 空间直线与平面(单元提升卷)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)上海市进才中学2022-2023学年高二上学期期中数学试题(已下线)数学(上海B卷)上海奉贤区致远高级中学2023届高三5月模拟数学试题(已下线)第06讲 立体几何位置关系及距离专题期末高频考点题型秒杀上海市黄浦区向明中学2023-2024学年高二上学期期中数学试题(已下线)考点15 立体几何中的折叠问题 2024届高考数学考点总动员【练】
2 . 如图,四面体ABCD中,△ABC是正三角形,△ACD是直角三角形,∠ABD=∠CBD,AB=BD.
(1)证明:平面ACD⊥平面ABC;
(2)设AB长为1,点E为BD的中点,求点D到平面ACE的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/31/c763ab53-0efc-4f7d-bcc4-cdac3423cde1.png?resizew=184)
(1)证明:平面ACD⊥平面ABC;
(2)设AB长为1,点E为BD的中点,求点D到平面ACE的距离.
您最近一年使用:0次
3 . 在如图所示的几何体中,四边形ABCD为菱形,
,
,
,
,
,点F在平面ABCD内的射影恰为BC的中点G.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/ba831ba5-1826-4024-8a16-eceb84a4b1b6.png?resizew=234)
(1)求证:平面
平面BED;
(2)求该几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117878cbd8c00f2aabcdf62b487e2dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeedb5f361a1baff6338436fff6c471d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60572975f9ac06ffc8d98ef94de49eb0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/3/ba831ba5-1826-4024-8a16-eceb84a4b1b6.png?resizew=234)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
(2)求该几何体的体积.
您最近一年使用:0次
2023-04-02更新
|
758次组卷
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3卷引用:第13章 立体几何初步(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)
第13章 立体几何初步(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)河南省安阳市2023届高三第二次模拟考试文科数学试题(已下线)期末复习07 空间几何线面、面面垂直-期末专项复习
4 . 如图,在直三棱柱
中,D是
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/9d561edd-f10f-45d8-b960-6724c66e3631.png?resizew=131)
(1)证明:
平面BCD.
(2)求点D到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f41d364b55d88688cd1f571ed231228.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/6/9d561edd-f10f-45d8-b960-6724c66e3631.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
(2)求点D到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
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2023-03-26更新
|
1188次组卷
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6卷引用:第13章 立体几何初步(A卷·基础提升练)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)
5 . 如图,直四棱柱
中,底面
为菱形,P为
的中点,M为
的中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/81216b32-a1dc-419e-8c5c-94c4915506b4.png?resizew=187)
(1)求证:
平面
;
(2)若
,求M到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/81216b32-a1dc-419e-8c5c-94c4915506b4.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014973e890e8f37de1bf8a050475d4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6e96872af0f0b341835576c407e364.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009d2e3f3738a95445be95445c06ee36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6e96872af0f0b341835576c407e364.png)
您最近一年使用:0次
2023-02-06更新
|
953次组卷
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3卷引用:专题8.17 立体几何初步全章综合测试卷(基础篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
(已下线)专题8.17 立体几何初步全章综合测试卷(基础篇)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)江西省重点中学协作体2023届高三下学期第一次联考数学(文)试题黑龙江省哈尔滨市第一中学校2022-2023学年高一下学期期中数学试题
名校
解题方法
6 . 如图,在三棱柱
中,
是边长为2的等边三角形,
,平面
平面
分别为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/c6445c5f-c5f9-49a1-bcb4-d7a94e49b79d.png?resizew=246)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若三棱柱
的体积为
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252143a7b900d33862f60b2536f6a8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12fa54e80fc52de0701cddc9a4ed47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ea285e96bf2e3b6406151bb694f10a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/c6445c5f-c5f9-49a1-bcb4-d7a94e49b79d.png?resizew=246)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2023-04-16更新
|
1649次组卷
|
4卷引用:第13章《立体几何初步》单元达标高分突破必刷卷(基础版)-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(苏教版2019必修第二册)
第13章《立体几何初步》单元达标高分突破必刷卷(基础版)-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(苏教版2019必修第二册)河南省商丘市部分学校2022-2023学年高中毕业班阶段性测试(六)文科数学试题宁夏银川市银川一中2024届高三上学期第五次月考数学(文)试题(已下线)第四章 立体几何解题通法 专题二 体积法 微点1 体积法(一)【基础版】
7 . 已知四边形ABCD中,
,
,O是AC的中点,将
沿AC翻折至
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/19/fc493409-cd14-4462-990e-b0f560333ab0.png?resizew=311)
(1)若
,证明:
平面ACD;
(2)若D到平面PAC的距离为
,求平面PAC与平面ACD夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba797c9497b139a93da88f88a768560.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23e6106e8c213b3f903fbc6b848ad5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/19/fc493409-cd14-4462-990e-b0f560333ab0.png?resizew=311)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a459372aa54090fcce9430a3cfa182f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
(2)若D到平面PAC的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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8 . 如图,四棱锥
的底面ABCD是平行四边形,平面
平面ABCD,
,
,
.O,E分别是AD,BC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/fd633d6c-c487-46f8-9749-14f1945ad895.png?resizew=182)
(1)证明:
平面POE;
(2)
,
,求点E到平面PCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/fd633d6c-c487-46f8-9749-14f1945ad895.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8c91e4c85a9da7f54b2237d870a50d.png)
您最近一年使用:0次
2023-04-15更新
|
1560次组卷
|
7卷引用:第13章《立体几何初步》单元达标高分突破必刷卷(基础版)-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(苏教版2019必修第二册)
解题方法
9 . 如图,
是正方形
所在平面外一点,
,且平面
平面
,
,
分别是线段
,
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65bb56e246c81bc125fc735727d00fb.png)
(2)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9946ad8ca073b5a746043a8de2104e7a.png)
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ff87102c14ae8c4c99c825ecf7d9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65bb56e246c81bc125fc735727d00fb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9946ad8ca073b5a746043a8de2104e7a.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2022-09-25更新
|
1755次组卷
|
5卷引用:第八章 立体几何初步 讲核心 02
(已下线)第八章 立体几何初步 讲核心 02江苏省南通市海门区2021-2022学年高一下学期期末数学试题(已下线)第03讲 直线、平面平行垂直的判定与性质(练)(已下线)期末专题09 立体几何大题综合-【备战期末必刷真题】【江苏专用】专题13立体几何与空间向量(第四部分)-高一下学期名校期末好题汇编
名校
解题方法
10 . 如图所示,在直角三角形
中,
,将
沿
折起到
的位置,使平面
平面
,点
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/16/3c368003-be69-463c-b8bc-ed7eedf6ddc4.png?resizew=266)
(1)证明:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e21e2956a7f315f5e7f4bc03c2c6793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac48b9ac8efbf41d6ab5242d247bd89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c42bce098904b241986bb91c65ab33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed30b73beeccafd4ec854237b33e1e2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/16/3c368003-be69-463c-b8bc-ed7eedf6ddc4.png?resizew=266)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6e5419274f6c330a1c8a021e565d6.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次
2023-05-13更新
|
1786次组卷
|
5卷引用:第六章 立体几何初步(单元综合检测卷)-【超级课堂】
第六章 立体几何初步(单元综合检测卷)-【超级课堂】河南省安阳市2023届高三三模文科数学试题四川省成都市树德中学2023届高三适应性考试文科数学试题(已下线)高一数学下学期期末模拟试题03-【同步题型讲义】四川省绵阳南山中学2023届高三仿真数学(文)试题