名校
解题方法
1 . 如图,在四棱锥
中,底面
是菱形,
平面
,
,
,
为
的中点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801459760177152/2802118573514752/STEM/60f060483da04840b3200d1b002325f5.png?resizew=211)
(1)求证:平面
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801459760177152/2802118573514752/STEM/60f060483da04840b3200d1b002325f5.png?resizew=211)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2021-09-06更新
|
676次组卷
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3卷引用:甘肃省兰州市第一中学2021-2022学年高三上学期11月防疫居家阶段检测数学(理科)试题
名校
2 . 如图,在三棱锥
中,
平面ABC,
,
,点E,F分别是AB,AD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/2e6cb80f-9086-4252-8a3a-cb421a0c9610.png?resizew=276)
(1)求证:
平面BCD;
(2)设
,求直线AD与平面CEF所成角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff7bd82b90112fa0f8383b069564b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/2e6cb80f-9086-4252-8a3a-cb421a0c9610.png?resizew=276)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927729940a1598d48e1b6ebc1c2f78ec.png)
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2021-08-17更新
|
2291次组卷
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12卷引用:甘肃省兰州市第一中学2021-2022学年高三上学期第一次月考(10月)数学(理)试题
甘肃省兰州市第一中学2021-2022学年高三上学期第一次月考(10月)数学(理)试题陕西省渭南市富平县2021届高三下学期二模理科数学试题湖北省黄石市大冶市第一中学2021-2022学年高二上学期10月月考数学试题陕西省部分名校2021-2022学年高三上学期10月月考理科数学试题陕西省汉中市校际联考2020-2021学年高二下学期期末理科数学试题广东省汕头市潮阳区棉城中学2021-2022学年高二上学期期中数学试题陕西省榆林市神木中学2021届高三下学期适应性考试理科数学试题安徽省合肥一六八中学2021-2022学年高二上学期第一次月考数学试题(已下线)专题19 空间向量与立体几何(解答题)-备战2022年高考数学(理)母题题源解密(全国甲卷)第一章 空间向量与立体几何单元测试(巅峰版)辽宁省大连部分重点高中2022-2023学年高二上学期10月月考数学试卷江苏省南通市通州区石港中学2022-2023学年高二下学期第三次阶段检测数学试题
3 . 在三棱锥
中,
是
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/f45c8074-1bed-400e-bfcd-189e8fa8fe86.png?resizew=156)
(1)证明:
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9978986377aae709a9da012e2782e9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/f45c8074-1bed-400e-bfcd-189e8fa8fe86.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f54161deed9fb6fa94318cd5a2efd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4294b7141d394654841008ac9b40dab.png)
您最近一年使用:0次
名校
4 . 如图,已知四棱锥
,
是等边三角形,
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/f1836a27-7e3a-4c92-9a07-b686f67a093d.png?resizew=152)
(1)求证:直线
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ae5f8381ffcce4281a0ca817b82a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/f1836a27-7e3a-4c92-9a07-b686f67a093d.png?resizew=152)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7175df06e33cad4e6bbc3f2f6b0a2986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2021-03-28更新
|
479次组卷
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3卷引用:甘肃省兰州市永登县第一中学2020-2021学年高三上学期期末数学试题
名校
5 . 如图,在三棱柱
中,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/1086a6ac-8473-4a59-a0a7-82ab95af2f97.png?resizew=164)
(1)证明:
平面ABC.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518a322494bd7624e6eed7fe290a2f9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/1086a6ac-8473-4a59-a0a7-82ab95af2f97.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89195bacd53d43195e70c12b5cfa041.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a824c242050a27d9da3bb3276ea99170.png)
您最近一年使用:0次
2020-07-11更新
|
430次组卷
|
4卷引用:甘肃省兰州外国语高级中学2021-2022学年高三上学期第一次适应性考试数学(理科)试题
名校
6 . 如图,在四棱锥
中,
为平行四边形,
,
平面
,且
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/97c57169-77b2-45fc-93b1-d98687a06cec.png?resizew=236)
(1)求证:
平面
;
(2)在线段
上(不含端点)是否存在一点
,使得二面角
的余弦值为
?若存在,确定
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf01adbdbab49dc9915b957ddf85351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb7b50091ad217f18db44fe0fc1550a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/97c57169-77b2-45fc-93b1-d98687a06cec.png?resizew=236)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4cb797a03b0d96fa146543101f993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-05-21更新
|
712次组卷
|
8卷引用:甘肃省兰州市外国语高级中学2022届高三上学期9月建标考试理科数学试题
7 . 如图1,在Rt△ABC中,∠C=90°,BC=3,AC=6,D,E分别是AC,AB上的点,且DE∥BC,DE=2.将△ADE沿DE折起到△A1DE的位置,使A1C⊥CD,如图2.
(2)若M是A1D的中点,求CM与平面A1BE所成角的大小;
(3)线段BC上是否存在点P,使平面A1DP与平面A1BE垂直?说明理由.
(2)若M是A1D的中点,求CM与平面A1BE所成角的大小;
(3)线段BC上是否存在点P,使平面A1DP与平面A1BE垂直?说明理由.
您最近一年使用:0次
2016-12-01更新
|
2919次组卷
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15卷引用:甘肃省兰州市第一中学2020-2021学年高二上学期期末考试数学(理)试题
甘肃省兰州市第一中学2020-2021学年高二上学期期末考试数学(理)试题2012年全国普通高等学校招生统一考试理科数学(北京卷)2016届四川省成都市新津中学高三上学期12月月考理科数学试卷江西省南昌市八一中学、洪都中学、麻丘中学等六校2016-2017学年高二5月联考数学(理)试题2018-2019人教A版高中数学选修2-1第三章 空间向量与立体几何 模块综合评价上海市张堰中学2018-2019学年高二下学期期中数学试题上海市复兴高级中学2015-2016学年高二下学期5月月考数学试题山东师范大学附属中学2020-2021学年高二10月月考数学试题(已下线)专题8.9 空间向量与立体几何单元测试卷-2021年新高考数学一轮复习学与练福建省漳州市第一外国语学校(漳州八中)2021-2022学年高二下学期期末考试数学试题北京理工大学附属中学2023届高三上学期12月月考数学试题广西贵港市西江高级中学2022-2023学年高二上学期10月模拟考试数学试题北京名校2023届高三二轮复习 专题四 立体几何 第3讲 立体几何的综合应用北京市顺义区第一中学2023-2024学年高二上学期10月考试数学试题(已下线)【一题多解】存在与否 向量探索