1 . 如图,在四棱锥E-ABCD中,
,M是EA的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016909089636352/3017503713886208/STEM/5a04b24ecf25469cae7207b1e912a8a6.png?resizew=190)
(1)证明:AE⊥平面
;
(2)若平面EAB
平面
,且
,三棱锥
的体积为
,求AB的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a2b96e63cc65119e7a49a9b4221789.png)
![](https://img.xkw.com/dksih/QBM/2022/7/6/3016909089636352/3017503713886208/STEM/5a04b24ecf25469cae7207b1e912a8a6.png?resizew=190)
(1)证明:AE⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f35614aff055b98b76ca262f64e629d.png)
(2)若平面EAB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66854bb5784c29a27075e884e10e392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df5f4a4225ec86ff419be333c3161a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d620f242099d9e5e3225115c80d9bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1083037647bea853ab5b73118f27ddd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
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2 . 如图所示,在四棱锥
中,BC//平面PAD,
,E是PD的中点.
(2)若M是线段CE上一动点,则线段AD上是否存在点
,使MN//平面PAB?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e306e30d3159e4a68435c3fcfc8da693.png)
(2)若M是线段CE上一动点,则线段AD上是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2022-02-10更新
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7卷引用:湖北省武汉市部分学校联合体(第十五中学等)2021-2022学年高二上学期期末数学试题
湖北省武汉市部分学校联合体(第十五中学等)2021-2022学年高二上学期期末数学试题重庆市天星桥中学2022届高三上学期学业质量调研抽测(一)数学试题(已下线)解密14 空间中的平行与垂直(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(全国通用)广东省东莞市丰泰外国语学校、麻涌中学等五校2021-2022学年高一下学期期中联考数学试题河南省济源市第四中学2022-2023学年高一下学期5月月考数学试题宁夏银川市第二中学2024届高三上学期统练四数学(文)试题安徽省阜阳市红旗中学2023-2024学年高一下学期第二次月考(5月)数学试题
3 . 如图,在四棱锥P−ABCD中,平面PAD⊥平面ABCD,点E为PC的中点,AB∥CD,CD⊥AD,CD=2AB=2,PA=AD=1,PA⊥AD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/1726103e-8532-4043-8f60-5e686403aa9f.png?resizew=296)
(1)证明:BE⊥平面PCD;
(2)求二面角P−BD−E的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/1726103e-8532-4043-8f60-5e686403aa9f.png?resizew=296)
(1)证明:BE⊥平面PCD;
(2)求二面角P−BD−E的余弦值.
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4 . 如图所示,在直三棱柱ABC-
,△ABC是边长为4的等边三角形,D、E、F分别为棱
、
、
的中点,点P在棱BC上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b248fcdeca2711790a7a2ed2c6bff4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/c8eda494-9350-4e9f-918a-1920e9379226.png?resizew=135)
(1)证明:AP∥平面DCE;
(2)求点B到平面APF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf78d12ef45a9934eb207a43b1a5dee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b248fcdeca2711790a7a2ed2c6bff4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/c8eda494-9350-4e9f-918a-1920e9379226.png?resizew=135)
(1)证明:AP∥平面DCE;
(2)求点B到平面APF的距离.
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2022-05-27更新
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743次组卷
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2卷引用:湖北省重点高中智学联盟2021-2022学年高一下学期5月联考数学试题
5 . 如图①,在梯形
中,
为
的中点,以
为折痕把
折起,连接
,得到如图②的几何体.
![](https://img.xkw.com/dksih/QBM/2022/8/27/3053817276620800/3054803314909184/STEM/caa9cc8e67a646e180f2fed2be87a663.png?resizew=346)
(1)证明:
;
(2)若四棱锥
的体积为2,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871727a2808e5a21e47f75484ec06da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://img.xkw.com/dksih/QBM/2022/8/27/3053817276620800/3054803314909184/STEM/caa9cc8e67a646e180f2fed2be87a663.png?resizew=346)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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2022-08-29更新
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3卷引用:湖北省荆荆宜三校2022-2023学年高三上学期起点考试数学试题
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6 . 已知在梯形ABCD中,AD∥BC,∠ABC=∠BAD=
,AB=BC=2AD=4,E,F分别是AB,CD上的点,EF∥BC,AE=2,沿EF将梯形ABCD翻折,使平面AEFD⊥平面EBCF(如图).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/c2114b62-069a-4568-a6d3-fc29a5089a09.png?resizew=286)
(1)证明:EF⊥平面ABE;
(2)求二面角D﹣BF﹣E的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/c2114b62-069a-4568-a6d3-fc29a5089a09.png?resizew=286)
(1)证明:EF⊥平面ABE;
(2)求二面角D﹣BF﹣E的余弦值.
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2022-06-14更新
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11卷引用:湖北省随州市曾都区第一中学2021-2022学年高一下学期期末模拟数学试题
湖北省随州市曾都区第一中学2021-2022学年高一下学期期末模拟数学试题(已下线)专题25 二面角相关问题训练-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)广东省广州市南武中学2023届高三上学期十月综合训练数学试题黑龙江哈尔滨市第一二二中学校2021-2022学年高一下学期期末数学试题(已下线)第八章 立体几何初步 (练基础)福建省泉州市第九中学2022-2023学年高二上学期入学考试数学试题新疆乌鲁木齐市第四中学2020-2021学年高二下学期期末数学(理)试题(已下线)立体几何专题:折叠问题中的证明与计算5种题型广东省东莞市东莞中学2022-2023学年高一下学期期中考试数学试题四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题(已下线)人教A版高二上学期【期中押题卷02】(测试范围:第1~2章)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
7 . 在四棱锥
中,底面
为矩形,
,平面
平面
,点
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/6b886c6d-76ef-4db3-a3d2-958428ee7838.png?resizew=151)
(1)证明:
;
(2)若
,四棱锥
的体积为
,求直线
与平面
所成角的余弦值.
![](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/63e4d19bf237a6fca67e0d01a9ddb726.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/6b886c6d-76ef-4db3-a3d2-958428ee7838.png?resizew=151)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b503c5da1208576c9fabd3685153c9d2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee76246dee4f1670e4f21e5eb393b52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519bd215d019509fa2d88e57f145a896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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8 . 如图,已知等腰梯形
中,
,
,
是
的中点,
,将
沿着
翻折成
,使平面
平面
.
平面
;
(2)求
与平面
所成的角;
(3)在线段
上是否存在点
,使得
平面
,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfb2735e1683a6ae86b5b97a0032e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619e1e12cc9037b65ec7ee72160e9022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f38a857b9fabe179c565feb88de4175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c60a0de546f75b46348265746aa707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbee3d2962bee74bf65ad4e71bca155.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1158eaa2e338f564eb18de5bef1d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257f33a7c02e440407ae57dc42de06e6.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb87785b2842459c59b2571aac7374b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324bc6bf263ca1feeaf1b61eddab330.png)
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2021-10-02更新
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8卷引用:湖北省黄冈市黄梅国际育才高级中学2022-2023学年高三上学期期中数学试题
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解题方法
9 . 如图,在四棱锥
中,四边形ABCD是平行四边形,点E,F,G分别为线段BC,PB,AD的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987113801785344/2988216381620224/STEM/41a1faf0-0a6c-4bf5-b1b0-809dc89872f7.png?resizew=222)
(1)证明:EF//平面PGC;
(2)在线段BD上找一点H,使得FH//平面PGC,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987113801785344/2988216381620224/STEM/41a1faf0-0a6c-4bf5-b1b0-809dc89872f7.png?resizew=222)
(1)证明:EF//平面PGC;
(2)在线段BD上找一点H,使得FH//平面PGC,并说明理由.
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2022-05-27更新
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1065次组卷
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6卷引用:湖北省重点高中智学联盟2021-2022学年高一下学期5月联考数学试题
名校
解题方法
10 . 如图,在直三棱柱
中,
,M,N分别为棱
、
的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987895392780288/2989391083978752/STEM/51871398-6d05-4475-91a8-63ecd7f0bfa9.png?resizew=207)
(1)证明:
平面
.
(2)求点B到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e73822adeeab22fdbd21b45faf85fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987895392780288/2989391083978752/STEM/51871398-6d05-4475-91a8-63ecd7f0bfa9.png?resizew=207)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
(2)求点B到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
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2022-05-28更新
|
1705次组卷
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7卷引用:湖北省十堰市2021--2022学年高一下学期期末数学试题