名校
解题方法
1 . 如图所示,在正方体
中,
为
中点.
![](https://img.xkw.com/dksih/QBM/2022/5/20/2983530540892160/2996090784448512/STEM/28ffc32a-0b0e-4f61-af28-e0cf2fc47692.png?resizew=179)
(1)求证:
平面
;
(2)若正方体棱长为2,求三棱锥
的体积.
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/2022/5/20/2983530540892160/2996090784448512/STEM/28ffc32a-0b0e-4f61-af28-e0cf2fc47692.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)若正方体棱长为2,求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0ca70467e7e330f513227455a10ec1.png)
您最近一年使用:0次
2022-06-07更新
|
1206次组卷
|
3卷引用:辽宁省丹东市凤城市第一中学2021-2022学年高一下学期6月月考数学试题
解题方法
2 . 如图,在直四棱柱
中,四边形
为菱形,且
为棱
上的一个动点.已知
.
![](https://img.xkw.com/dksih/QBM/2022/7/20/3026528109469696/3027496018485248/STEM/604f4341084a45469a88aafca1c763b0.png?resizew=164)
(1)当
点为
的中点时,证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
平面
;
(2)若平面
平面
,求
的长.
![](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/648a8dc609b4c4add5e4416ab0ed2b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed5e5d514bba98dbd038d0857a34ef7.png)
![](https://img.xkw.com/dksih/QBM/2022/7/20/3026528109469696/3027496018485248/STEM/604f4341084a45469a88aafca1c763b0.png?resizew=164)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c54d01623f09f23103f03ba1135fc6a.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c54d01623f09f23103f03ba1135fc6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
3 . 如图1,在直角梯形ABCD中,
,
,
,
,E在AB上,且
为边长为2的等边三角形.将
沿DE折起,使得点A到点P的位置,平面
平面BCDE,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/24/4fdb590d-732c-43c5-80d9-2e3e758ec35b.png?resizew=304)
(1)若F为PC的中点,证明
平面PDE;
(2)证明:
;
(3)求直线BP与平面DCBE所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d9142db4dd2ef151bf3d4a63afb61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac48b9ac8efbf41d6ab5242d247bd89.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/24/4fdb590d-732c-43c5-80d9-2e3e758ec35b.png?resizew=304)
(1)若F为PC的中点,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d888c0b616792a2c41ff180de99fbb.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
(3)求直线BP与平面DCBE所成角的大小.
您最近一年使用:0次
名校
解题方法
4 . 如图,在四棱锥
中,
是边长为2的等边三角形,梯形
满足
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982704490872832/2995536316547072/STEM/67246644-e9b1-4f9b-a933-931968ec1449.png?resizew=176)
(1)求证:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/19/2982704490872832/2995536316547072/STEM/67246644-e9b1-4f9b-a933-931968ec1449.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfacd208d769d01f1d4ef20313cd869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e77e93fb69b4c0716dde86f52e7406.png)
您最近一年使用:0次
2022-06-06更新
|
943次组卷
|
5卷引用:辽宁省铁岭市六校协作体2021-2022学年高一下学期期末联考数学试题
辽宁省铁岭市六校协作体2021-2022学年高一下学期期末联考数学试题江西省赣州市教育发展联盟2021-2022学年高二下学期第8次联考数学(文)试题(已下线)2022年全国高考甲卷数学(文)试题变式题9-12题重庆市实验中学校2021-2022学年高一下学期期末复习(三)数学试题(已下线)2022年全国高考甲卷数学(文)试题变式题17-20题
名校
解题方法
5 . 如图,已知四棱锥
中,平面
平面
,底面
为矩形,且
,
,
,O为棱AB的中点,点E在棱AD上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8eb491b9-25ff-4831-8f9d-42d4f31afc2f.png?resizew=172)
(1)证明:
;
(2)在棱PB上是否存在一点F使
平面
?若存在,请指出点F的位置并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7005932de8ace6e3c78a754c35466d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940099db7ffe6b3f7e70afcfba66750a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8eb491b9-25ff-4831-8f9d-42d4f31afc2f.png?resizew=172)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5ffe436f8eb53a211abf95baed8ca9.png)
(2)在棱PB上是否存在一点F使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e447c70f2ad6d6a38afd6cad312007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
您最近一年使用:0次
2022-07-13更新
|
892次组卷
|
5卷引用:辽宁省锦州市2021-2022学年高一下学期期末数学试题
辽宁省锦州市2021-2022学年高一下学期期末数学试题(已下线)第03讲 空间直线、平面的平行 (精讲)-2江西省遂川中学2022-2023学年高二上学期期末考试数学试题辽宁省鞍山市一般高中协作校(含矿山高级中学、文化学校等)2022-2023学年高一下学期6月月考数学试题(已下线)模块四 专题1 期末重组综合练(辽宁)(人教B)
名校
6 . 已知四棱锥
,底面ABCD是平行四边形,且
.侧面PCD是边长为2的等边三角形,且平面
平面ABCD.点E在线段PC上,且直线
平面BDE.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2986877546536960/2988536820776960/STEM/d1788710-ed63-4af3-94cb-31a89d625021.png?resizew=232)
(1)求证:
;
(2)设二面角
的大小为
,且
.求直线BE与平面ABCD所成的角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf439f019342d3cb60dcb9254bb6645f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2986877546536960/2988536820776960/STEM/d1788710-ed63-4af3-94cb-31a89d625021.png?resizew=232)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec78c2154c5972efd438a6555afaf2d.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0455c5f4c74102072e3f987a43cdb3e.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,四棱锥
中,底面ABCD为平行四边形,E是PD上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/03f28427-70af-4bac-9c6e-b862903850f7.png?resizew=203)
(1)若E、F分别是PD和BC中点,求证:
平面PAB;
(2)若
平面AEC,求证:E是PD中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/03f28427-70af-4bac-9c6e-b862903850f7.png?resizew=203)
(1)若E、F分别是PD和BC中点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
您最近一年使用:0次
2022-05-15更新
|
2021次组卷
|
6卷引用:辽宁省渤海大学附属高级中学2021-2022学年高一下学期第二次阶段性考试数学试题
名校
解题方法
8 . 如图所示,在直三棱柱
中,
是
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
平面
;
(2)设
,求几何体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1d6750e4b38ecfae78c0eed96153b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e9f157d1d7cfb37741825e3e9bcb9c.png)
您最近一年使用:0次
2022-06-20更新
|
1218次组卷
|
4卷引用:辽宁省六校协作体2021-2022学年高一下学期第三次联合考试数学试题
辽宁省六校协作体2021-2022学年高一下学期第三次联合考试数学试题(已下线)第31讲 空间几何体体积及点到面的距离问题4种题型(已下线)8.5.2 直线与平面平行(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)陕西省西安中学2022-2023学年高一下学期期中考试数学试题
名校
解题方法
9 . 如图,在圆锥
中,
,
,
为底面圆上的三个点,
,且
,
.
![](https://img.xkw.com/dksih/QBM/2022/6/4/2994043545329664/2997667445112832/STEM/d0fd3f8b-04c6-4d44-a45b-a8bc34ed6683.png?resizew=200)
(1)证明:
平面
.
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a3028dd2e40f2fddfef3f5f85998c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ee79cc41f02dbaa25da31c601601da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0b8c5975f7d4ebd9585097c07c121f.png)
![](https://img.xkw.com/dksih/QBM/2022/6/4/2994043545329664/2997667445112832/STEM/d0fd3f8b-04c6-4d44-a45b-a8bc34ed6683.png?resizew=200)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d27ff0b39832f094ec51e28721d739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6aeaf411b82c8a3b2770ac1262cc62.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbf5e17b1e560fe03649e2591cad131.png)
您最近一年使用:0次
2022-06-09更新
|
925次组卷
|
4卷引用:辽宁省抚顺市第一中学2021-2022学年高一下学期6月月考数学试题
辽宁省抚顺市第一中学2021-2022学年高一下学期6月月考数学试题河南省豫西部分名校2021-2022学年高一下学期月考数学试题山东省2021-2022学年高一下学期选课走班质量检测数学试题(已下线)专题22 空间中的平行关系(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)
10 . 如图,四棱锥
中,侧面
为等边三角形且垂直于底面
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/23/2985727444746240/2989396544397312/STEM/8c3ee4eaa60b4f8baef12e8e6a1db9a8.png?resizew=259)
(1)证明:
;
(2)若
面积为
,求点
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78aafccd397e9c88a567abf4993d40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7af36689a2d2a5f999b3b5859a3c9faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61588617d22abd00af4ca489bb3a8787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2022/5/23/2985727444746240/2989396544397312/STEM/8c3ee4eaa60b4f8baef12e8e6a1db9a8.png?resizew=259)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04fb30a9d07e410ac92c34b8ad0133db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2022-05-28更新
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853次组卷
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3卷引用:辽宁省沈阳市第二中学2021-2022学年高一下学期6月月考数学试题