名校
解题方法
1 . 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
|
1207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
2 . 如图,在直三棱柱
中,M、N分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/2022/2/20/2920256761511936/2929650816516096/STEM/8009507e49b1469fb2eaed98dadc60bd.png?resizew=152)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)若
,
,求证:MN⊥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/2022/2/20/2920256761511936/2929650816516096/STEM/8009507e49b1469fb2eaed98dadc60bd.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686849a983d24dd62270b2967708cc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2022-03-05更新
|
715次组卷
|
3卷引用:辽宁省沈阳市重点高中协作体2021-2022学年高一下学期期末数学试题
辽宁省沈阳市重点高中协作体2021-2022学年高一下学期期末数学试题(已下线)期中模拟卷-2021-2022学年高一数学链接教材精准变式练(人教A版2019必修第二册)江苏省南京市第五中学2021-2022学年高二上学期10月月考数学试题
3 . 如图,在四棱锥
中,
平面ABCD,四边形ABCD为正方形,点F为线段PC上的点,过A,D,F三点的平面与PB交于点E.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/894b02c4-dd15-49f0-9bbe-8d370313ac03.png?resizew=197)
(1)证明:
平面ABCD;
(2)若E为PB中点,且
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/15/894b02c4-dd15-49f0-9bbe-8d370313ac03.png?resizew=197)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)若E为PB中点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96127e45e2dd2494fccb1c0905951f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a55bb66c6d34e16140549f53ffe774.png)
您最近一年使用:0次
2013·山东·一模
名校
解题方法
4 . 如图所示,已知
平面ACD,
平面ACD,
为等边三角形,
,F为CD的中点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/35cb2e1c-0183-4e19-b23b-ee240a0a6992.png?resizew=169)
(1)
平面BCE;
(2)平面
平面CDE.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb59a3752da728cfa77557dd14d0f737.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/35cb2e1c-0183-4e19-b23b-ee240a0a6992.png?resizew=169)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9c89e28bb3b5ce434e8ebea6363339.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
您最近一年使用:0次
2022-02-26更新
|
3552次组卷
|
27卷引用:第十一章 立体几何初步 单元检测卷
第十一章 立体几何初步 单元检测卷(已下线)专题8.2 立体几何初步 章末检测2(中)-【满分计划】2021-2022学年高一数学阶段性复习测试卷(人教A版2019必修第二册)(已下线)第八章 立体几何初步(基础训练)A卷-2021-2022学年高一数学课后培优练(人教A版2019必修第二册)贵州省黔西南州2021-2022学年高一下学期期末质量检测数学试题(已下线)2013届山东省高三高考压轴文科数学试卷(已下线)2015高考数学(理)一轮配套特训:7-5直线、平面垂直的判定及性质2016届河南郑州一中教育集团高三文押题二数学试卷2017届江西省鹰潭市高三第一次模拟考试数学(文)试卷2017届江西省南昌市十所省重点中学命制高三第二次模拟突破冲刺二数学(文)试卷江西省九江第一中学2016-2017学年高二下学期期中考试数学(文)试题河北省枣强中学2016-2017学年高二下学期期末考试数学(文)试题(已下线)2017-2018学年第一学期期末复习备考之精准复习模拟题高一人教版(必修一+必修二)数学试题(B卷)山东省夏津一中2019届高三上学期12月月考数学(文)试题(已下线)7-5 直线、平面垂直的判定及其性质(高效训练)-2019版导学教程一轮复习数学(人教版)(已下线)江西省鹰潭市2017届高三第一次模拟考试文数试题(已下线)专题42 空间点、直线、平面的位置关系综合练习-2021年高考一轮数学(理)单元复习一遍过(已下线)专题42 空间点、直线、平面的位置关系综合练习-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题42 空间点、直线、平面的位置关系综合练习-2021年高考一轮数学(文)单元复习一遍过西藏自治区拉萨中学2020-2021学年高一下学期期末考试数学试题甘肃省金昌市永昌县第一高级中学2021-2022学年高三上学期12月月考数学文科试题河南濮阳市华龙区高级中学2021-2022学年高三上学期开学考试数学文科试题吉林省长春市第二实验中学2022-2023学年高一下学期期中考试数学试题河南省南阳市卧龙区博雅学校2022-2023学年高一下学期6月月考数学试题四川省成都市锦江区嘉祥外国语高级中学2022-2023学年高一下学期6月月考数学试题广东省深圳市第二高级中学2023-2024学年高二上学期第一学段考试数学试题(已下线)宁夏回族自治区石嘴山市第三中学2022-2023学年高一下学期期末考试数学试卷宁夏石嘴山市第三中学2022-2023学年高一下学期期末数学试题
名校
解题方法
5 . 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
|
924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)
6 . 如图,在直三棱柱
中,
,且
,
,
,
是棱
的中点,
是棱
上的点,满足
.
![](https://img.xkw.com/dksih/QBM/2022/7/19/3025835179589632/3026888124522496/STEM/7a892ba0c1dc4292b7d5202c2dcff261.png?resizew=145)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022365ed188bd800e0b8a2b4ec1e2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.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/e840e386b2870205de3c7a21f97668e4.png)
![](https://img.xkw.com/dksih/QBM/2022/7/19/3025835179589632/3026888124522496/STEM/7a892ba0c1dc4292b7d5202c2dcff261.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
您最近一年使用:0次
解题方法
7 . 如图,四面体
中,E是
的中点,点F在
上,
平面
,平面
与平面
的交线为l,
,
,证明:
![](https://img.xkw.com/dksih/QBM/2022/7/19/3025781012488192/3026876819144704/STEM/9c507a963ffe4202aa2ea7f34f60e212.png?resizew=213)
(1)
;
(2)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a651eb577dbada1f29590e558d6f9fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650c6c818df102a83ce5159e3208d01a.png)
![](https://img.xkw.com/dksih/QBM/2022/7/19/3025781012488192/3026876819144704/STEM/9c507a963ffe4202aa2ea7f34f60e212.png?resizew=213)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5b5c88bed3eb4d5eb2f2a5d25f0bc1.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
您最近一年使用:0次
名校
解题方法
8 . 在四棱锥
中,底面
是正方形,
与
交于点
,
平面
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/090ff910-af51-4742-b44a-14aa6d7a1f3d.png?resizew=156)
(1)求证:
平面
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f09ad78d4eccd1a9c9ccd3c4af79c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/090ff910-af51-4742-b44a-14aa6d7a1f3d.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84be64d28b1623e71ad989f37336b1f2.png)
您最近一年使用:0次
2021-12-29更新
|
687次组卷
|
5卷引用:辽宁省朝阳市育英高级中学2021-2022学年高二上学期期末数学试题
名校
9 . 如图所示,四面体
中,已知平面
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/19/2875916882313216/2876514778742784/STEM/77717152c036426bbc1a6fd8950ad9c5.png?resizew=222)
(1)求证:
.
(2)若二面角
为
,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309e58bf083bad13abd549720a63a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f0d3d800ff70b765756ead8ca8d089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bae5203f4b4acf23779114b3466e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58899f5c3638f1e32274137723f99836.png)
![](https://img.xkw.com/dksih/QBM/2021/12/19/2875916882313216/2876514778742784/STEM/77717152c036426bbc1a6fd8950ad9c5.png?resizew=222)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc1f76257275ab4b04f9bc913535670.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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2021-12-20更新
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635次组卷
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4卷引用:辽宁省沈阳市第二中学2021-2022学年高二上学期期末数学试题
名校
解题方法
10 . 如图,在四棱锥
中,
平面
,四边形
为正方形,点
为线段
上的点,过
三点的平面与
交于点
.
![](https://img.xkw.com/dksih/QBM/2022/6/21/3006136152711168/3007423673647104/STEM/37b25bb38f5d4e70a6d37aff61a1d1d4.png?resizew=179)
(1)证明:
平面
:
(2)若
为
中点,且
,求平面
将四棱锥分成两部分的体积比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7065622bc61d9c2fc2847fe17eebc9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2022/6/21/3006136152711168/3007423673647104/STEM/37b25bb38f5d4e70a6d37aff61a1d1d4.png?resizew=179)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a109c829d652632a88ade6924fcda206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08c14e87a2bcf7090eab2fea73667d2.png)
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