名校
解题方法
1 . 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.
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2022-05-02更新
|
305次组卷
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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
2 . 如图,在直棱柱
中,底面四边形
为边长为
的菱形,
,E为AB的中点,F为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/fb86a6c9-cc94-40bc-a223-4b42e20d0919.png?resizew=154)
(1)证明:
平面
;
(2)若点P为线段
上的动点,求点P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/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc633603ce426facfd47d2bca6a90dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/fb86a6c9-cc94-40bc-a223-4b42e20d0919.png?resizew=154)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(2)若点P为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
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2022-11-04更新
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1458次组卷
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9卷引用:江西省赣州市教育发展联盟2023届高三上学期第9次联考(12月)数学(文)试题
3 . 如图,在四棱锥
中,底面ABCD是正方形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/7afde5fc-a045-4899-af2c-1df40cdfa3b0.png?resizew=187)
(1)证明:平面
平面
;
(2)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531496172673a735ddf36284fa45fb81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0051d92c8639713847682826c2bb9783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5a20de5ab5d40c465b0353fe3c5e589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66536456c67fce11a510d3dad864dc2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/7afde5fc-a045-4899-af2c-1df40cdfa3b0.png?resizew=187)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cc199e2f29f643482f19d8b345ea54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ef387d93efb947fbe046f5f19703e7.png)
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2022-10-26更新
|
503次组卷
|
4卷引用:江西省丰城中学、新余一中2023届高三上学期联考数学(文)试题
4 . 如图,在四棱锥P-ABCD中,底面ABCD为正方形,侧面PAD是正三角形,平面PAD⊥平面ABCD,M、O、N分别是PD、AD、BC的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/27/2903417327665152/2938378216120320/STEM/b19a1b851ce1479999a14f030b1d7fd9.png?resizew=162)
(1)证明:平面PAB∥平面MON;
(2)若AB=2,求点C到平面PAB的距离.
![](https://img.xkw.com/dksih/QBM/2022/1/27/2903417327665152/2938378216120320/STEM/b19a1b851ce1479999a14f030b1d7fd9.png?resizew=162)
(1)证明:平面PAB∥平面MON;
(2)若AB=2,求点C到平面PAB的距离.
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2022-03-17更新
|
642次组卷
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4卷引用:江西省宜春市上高二中2021-2022学年高二4月第五次月考数学(文)试题
5 . 如图,四棱柱
的底面
为平行四边形,其中
平面
,
,
,
分别为线段
,
的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878777900204032/2880248007647232/STEM/ae4500928ffb45099f012b126ecc5eda.png?resizew=231)
(1)求证:平面
平面
;
(2)若
,
,求点
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/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2021/12/23/2878777900204032/2880248007647232/STEM/ae4500928ffb45099f012b126ecc5eda.png?resizew=231)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038b970e78494969975c94dc53a33c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9615856aad70897e3d4c0b91a865d799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
您最近一年使用:0次
6 . 已知四边形
是梯形(如图甲).AB∥CD,AD⊥DC,CD=4,AB=AD=2,E为CD的中点,以AE为折痕把
折起,使点D到达点P的位置(如图乙),且PB=2.
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872466576834560/2879689875202048/STEM/9a795877f6b04d77b6e867c7e10b3156.png?resizew=351)
(1)求证:平面
平面
;
(2)求点A到平面PBE的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872466576834560/2879689875202048/STEM/9a795877f6b04d77b6e867c7e10b3156.png?resizew=351)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
(2)求点A到平面PBE的距离.
您最近一年使用:0次
2021-12-24更新
|
368次组卷
|
7卷引用:江西省吉安市安福二中、吉安县三中、井大附中2021-2022学年高二上学期12月份三校联考数学(文)试题
名校
解题方法
7 . 如图,在四棱锥P-ABCD中,PA⊥底面ABCD,AD∥BC,∠DAB=90°,AB=BC=
=2,E为PB的中点,F是PC上的点.
(2)求点C到平面PBD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c605f428994894bf0b0d9f066ac7495c.png)
(2)求点C到平面PBD的距离.
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2022-10-04更新
|
596次组卷
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15卷引用:五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题1
五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题1江西省贵溪市实验中学2020-2021学年高二12月月考理科数学试题五岳(湖南、河南、江西)2019-2020学年高三下学期3月线上联考数学(文)试题22020届河南省高三4月第三次在线网上联考文科数学2020届河南省高三下学期第三次(4月份)联考(文科) 数学试题江西省贵溪市实验中学2020-2021学高二上学期期中考试数学(理)试题河南省中原名校联盟2021-2022学年高二上学期第二次适应性联考理科数学试题江苏省南京市金陵中学2022-2023学年高二上学期10月月考数学试题江西省赣州市赣县第三中学2022-2023学年高二上学期期中测试数学试题湖南省永州市第一中学2023-2024学年高一下学期5月月考数学试卷2020届福建连城县第一中学高三4月模拟考试数学(文)试题2020届宁夏银川市第九中学高三下学期第二次模拟考试数学(文)试题吉林省通钢一中、集安一中、梅河口五中等省示范高中2020届高三(5月份)高考数学(文科)模拟试题四川省泸州市江阳区2021-2022学年高三上学期期末数学文科试题(已下线)第03讲 直线、平面平行垂直的判定与性质(讲)
名校
解题方法
8 . 如图,在四棱锥
中,
,
,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/d3fcbb62-66d4-44cb-a135-eea80c3adfc1.png?resizew=169)
(1)证明:
平面PDC.
(2)若E是棱PA的中点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
平面PCD,求点D到平面PAB的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25267f04873339a85a74c29e77ec2fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0717c99cf54077d805c71254fa3230d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eef0eaf87646c1692bdae799d194d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/d3fcbb62-66d4-44cb-a135-eea80c3adfc1.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95475bfc06e884754eb4a455c3f434e.png)
(2)若E是棱PA的中点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
您最近一年使用:0次
2022-07-05更新
|
1196次组卷
|
12卷引用:江西省上高二中2022-2023学年高二上学期8月数学试题
江西省上高二中2022-2023学年高二上学期8月数学试题贵州省遵义市道真仡佬族苗族自治县民族高级中学2022-2023学年高二上学期第一次月考数学试题河南省南阳地区2021-2022学年高一下学期期终摸底考试数学试题湖南省衡阳市部分校2021-2022学年高一下学期期末数学试题河北省邢台市2021-2022学年高一下学期期末数学试题广西贵港市2021-2022学年高一下学期期末教学质量监测数学试题吉林省白山市2021-2022学年高一下学期期末数学试题河北省承德市2021-2022学年高一下学期期末数学试题云南省楚雄州2021-2022学年高一下学期期末教育学业质量监测数学试题内蒙古自治区巴彦淖尔市2021-2022学年高一下学期期末数学试题广东省清远市2021-2022学年高一下学期期末数学试题广东省连南瑶族自治县民族高级中学2022-2023学年高一下学期期中数学试题
9 . 如图,在棱长为a的正方体ABCD-A1B1C1D1中,E、F分别是AA1与CC1的中点.
平面FBD;
(2)求平面EB1D1与平面FBD之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
(2)求平面EB1D1与平面FBD之间的距离.
您最近一年使用:0次
10 . 如图1,在直角梯形ABCD中,
,
,且
,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翻折,使
,M为ED的中点,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/a79dd867-e81b-4a2d-9694-7496a0f02b80.png?resizew=511)
(1)求证:平面
平面BDE;
(2)若
,求D到平面BEC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3da6e90f9c9617cd495abb57ab9b0e0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/a79dd867-e81b-4a2d-9694-7496a0f02b80.png?resizew=511)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82773737609e65dea3c5c67099f1b10d.png)
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