名校
解题方法
1 . 如图,在四棱锥
中,
底面ABCD,底面ABCD为平行四边形,
,
,
且
,E是PD中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/87be47fb-1f19-4567-877a-f84183505458.png?resizew=218)
(1)求证:
平面AEC;
(2)求直线PC与平面ACE所成角的正弦值;
(3)在线段PB上(不含端点)是否存在一点M,使得二面角
夹角的余弦值为
?若存在,确定M的位置;若不存在,说明理由.
![](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/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4f3da376bd01ef33579e6eecc6f047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/87be47fb-1f19-4567-877a-f84183505458.png?resizew=218)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
(2)求直线PC与平面ACE所成角的正弦值;
(3)在线段PB上(不含端点)是否存在一点M,使得二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4cb797a03b0d96fa146543101f993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
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2023-01-05更新
|
484次组卷
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2卷引用:新疆乌鲁木齐八一中学2022-2023学年高二上学期期末考试数学试题
名校
2 . 在四棱锥
中,E为棱AD的中点,PE⊥平面
,
,
,
,
,F为棱PC的中点.
(1)求证:
平面
;
(2)若二面角
为
,求直线
与平面
所成角的正切值.
![](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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ac29b5b40502851b7a24f7ebcc0b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbd8e8c759858fb3d3132605d44e865.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/e58d7955-983f-4ce0-908a-2e62e1e81ea2.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea81cfad5da39884e84d257149d7f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2024-01-14更新
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533次组卷
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7卷引用:新疆喀什地区岳普湖县2022届高三第一次模拟考试数学(文)试题
新疆喀什地区岳普湖县2022届高三第一次模拟考试数学(文)试题山西省大同市第一中学校2021-2022学年高二上学期10月月考数学试题广东省茂名市第五中学2021-2022学年高二上学期期中数学试题江苏省扬州市高邮市第一中学2021-2022学年高三上学期期中模拟数学试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-2(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【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)山东省济宁市第一中学2024届高三上学期期末数学试题
3 . 如图,在四棱锥
中,
平面
,
,
为等边三角形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/ca0a51c4-f6e4-4288-9b5d-806a6f5da742.png?resizew=155)
(1)求证:
平面
,且
平面
.
(2)已知
,
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1c122603b60b6f1a1334ddb56c3fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a682c80413bd845f60f58362a6d766.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/ca0a51c4-f6e4-4288-9b5d-806a6f5da742.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
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2022-06-06更新
|
999次组卷
|
4卷引用:新疆昌吉州行知学校2023届高三上学期期末考试数学(理)试题
新疆昌吉州行知学校2023届高三上学期期末考试数学(理)试题2022年普通高等学校招生全国统一考试临考押题密卷(B)理科数学试题(已下线)2022年全国新高考II卷数学试题变式题13-16题(已下线)2022年全国新高考II卷数学试题变式题20-22题
名校
解题方法
4 . 如图,在长方体ABCD-A1B1C1D1中,AB=2BC=2CC1=2,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076339012116480/3076375830126592/STEM/9d473c73ff1c4065916be317fc21c5c5.png?resizew=266)
(1)求点D到平面AD1E的距离;
(2)求证:平面AD1E⊥平面EBB1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/2022/9/28/3076339012116480/3076375830126592/STEM/9d473c73ff1c4065916be317fc21c5c5.png?resizew=266)
(1)求点D到平面AD1E的距离;
(2)求证:平面AD1E⊥平面EBB1.
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2022-09-28更新
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6卷引用:新疆维吾尔自治区和田地区洛浦县2022-2023学年高二上学期11月期中数学试题
名校
5 . 如图,四边形ABCD是圆柱的轴截面,
,O分别是上、下底面圆的圆心,EF是底面圆的一条直径,DE=DF.
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943275657469952/2943887327248384/STEM/6733c25cd9b3432e834d1091d18c5e34.png?resizew=254)
(1)证明:EF⊥AB;
(2)若
,求平面BCF与平面CDE所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://img.xkw.com/dksih/QBM/2022/3/24/2943275657469952/2943887327248384/STEM/6733c25cd9b3432e834d1091d18c5e34.png?resizew=254)
(1)证明:EF⊥AB;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb37765c3d5d6b74791358200a834a67.png)
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2022-03-25更新
|
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|
5卷引用:新疆昌吉学联体2022届高三下学期第三次高考适应性联考数学(理)试题
名校
6 . 在四棱锥
中,底面ABCD是等腰梯形,
,
,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/3fddd46f-f511-43df-ad16-9b16f395655d.png?resizew=155)
(1)求证:
为直角三角形;
(2)若
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a8b1c432c1266ec43fb9a78f7a77fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b77a5c3865855fbb3d24f9522ced8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3c74b930d4e691b519965e436f2c37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/3fddd46f-f511-43df-ad16-9b16f395655d.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da7bcea5a45eeae211f5851f12a7517.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e4e97a4bd7675f12f73266254dd435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc407e2b3e9da16eba881fd7a83845a.png)
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2023-01-06更新
|
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2卷引用:新疆部分学校2023届高三上学期第一次联考数学(理)试题
名校
解题方法
7 . 在直角梯形
中,
,A为线段
的中点,四边形
为正方形.将四边形
沿
折叠,使得
,得到如图(2)所示的几何体.
与平面
所成角的正弦值;
(2)当F为线段
的中点时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b2b35cea8278afb6146c15b1040e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4e97715e80793d4ea53012eb409cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd5861601a5e5aaa35dc70b902fd381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db27b7f29d7d01b2692f217bc3079fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
(2)当F为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baa2f1a925d67fcd406218b83015d13.png)
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2022-07-01更新
|
905次组卷
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6卷引用:新疆实验中学2022-2023学年高二上学期期中考试数学试题
解题方法
8 . 已知正方体
的棱长为1,
、
分别为棱
、
的中点,
为棱
上的动点,
为线段
的中点.则下列结论中正确序号为______ .
①
;②
平面
;③
的余弦值的取值范围是
;④△
周长的最小值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe89951021988a68b8eda8d98c5c5570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a66d1d242f5317fcc90fee9a8e9fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52173c8cc44246823c2bee21a783b731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46060ff16376f584eb554e09686ab703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0814258cf5e34be916ea7774e896738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06ed3e88f623ed9313d06b1bb2a87ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0487690814e606b108853b9ed32de87.png)
您最近一年使用:0次
10-11高二下·河北石家庄·阶段练习
名校
9 . 如图,在四棱锥
中,底面
是矩形,
平面
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/9b5daffd-7dd5-4d39-a63f-cc8d12a7d181.png?resizew=228)
(1)证明:
平面
;
(2)求平面
与平面
夹角的大小.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbca3f97adcf5eca55b4063d018d7b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2682f3f3f0f72c893b99073bcac83ff2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/9b5daffd-7dd5-4d39-a63f-cc8d12a7d181.png?resizew=228)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e20dda43344207b7bd135e889e2b967.png)
您最近一年使用:0次
2021-11-05更新
|
1419次组卷
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16卷引用:新疆乌苏市第一中学2021-2022学年高二3月月考数学(理)试题
新疆乌苏市第一中学2021-2022学年高二3月月考数学(理)试题山东省济南外国语学校2021-2022学年高二上学期期中数学试题湖北省黄石市有色第一中学2021-2022学年高二下学期期中数学试题福建省厦门海沧实验中学2021-2022学年高二下学期3月阶段性检测数学试题福建省建瓯市芝华中学2022-2023学年高二上学期期中考试数学试题河南省禹州市开元学校2022-2023学年高二上学期网课期中考试数学试题(已下线)2010-2011年河北省正定中学高二下学期第一次月考数学理卷(已下线)2010-2011年四川省成都市玉林中学高二下学期3月月考数学理卷(已下线)2013-2014学年河北正定中学高二下学期第一次月考数学卷甘肃省武威第十八中学人教A版数学选修2-1单元检测:第三章 空间向量与立体几何河北省昌黎县汇文二中2021-2022学年高二上学期10月月考数学试题河北省石家庄实验中学2021-2022学年高二上学期10月月考数学试题 湖南省常德市临澧县第一中学2021-2022学年高二上学期期中数学试题福建省莆田第一中学2021-2022学年高二上学期期中考试数学试题广东省佛山市南海区里水高级中学2021-2022学年高二上学期第二次教学质量检测数学试题湖南省益阳市箴言中学2021-2022学年高二上学期第三次月考数学试题
名校
10 . 已知正方体
,棱长为1,
分别为棱
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5307e04a84a0621e4d5bd2aaa1980ef.png)
A.直线![]() ![]() | B.![]() |
C.直线![]() ![]() ![]() | D.三棱锥![]() ![]() |
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2022-11-26更新
|
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