1 . 如图,四棱锥P-ABCD中,底面ABCD是平行四边形,AD
BD,AB=2AD,且PD⊥底面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/16/e146c52f-4621-4df7-a43c-6c3adb32167b.png?resizew=196)
(1)证明:平面PBD⊥平面PBC;
(2)若二面角P-BC-D为
,求AP与平面PBC所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/16/e146c52f-4621-4df7-a43c-6c3adb32167b.png?resizew=196)
(1)证明:平面PBD⊥平面PBC;
(2)若二面角P-BC-D为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
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12卷引用:甘肃省白银市会宁县2018-2019学年高二上学期期末考试数学(理)试题
甘肃省白银市会宁县2018-2019学年高二上学期期末考试数学(理)试题安徽省滁州市2018-2019学年高二第一学期期末联考(理科)数学试题黑龙江省齐市地区普高联谊2018~2019学年高二上学期期末考试数学(理)试卷河南省新乡、焦作市部分学校联考2020-2021学年高二上学期12月月考数学(理)试题山西省大同市浑源中学2021-2022学年高二下学期期中数学试题云南省弥勒市第四中学2022-2023学年高二下学期3月月考数学试题辽宁省朝阳市北票市高级中学2022-2023学年高二下学期3月月考数学试题重庆市万州第二高级中学2022-2023学年高二下学期期中数学试题(已下线)高二数学下学期期中模拟试卷(第6章-第8章,含数列和导数)-【题型分类归纳】2022-2023学年高二数学同步讲与练(苏教版2019选择性必修第二册)贵州省黔西南州安龙县第四中学2022-2023学年高二下学期期中考试数学试题云南省曲靖市富源县第八中学2022-2023学年高二下学期期中考试数学试题贵州省黔西南州兴义市顶效开发区顶兴学校2022-2023学年高二下学期3月月考数学试题
名校
解题方法
2 . 如图,四棱锥
中,
底面ABCD,
为等边三角形,
,
,M是PB上一点,且
,N是PC的中点.
(1)求证:
;
(2)若二面角
的大小为
,求三棱锥
的体积.
![](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/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f1900a198a668b3e3c4fda8def209a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0b9ae1fdf6b88a97ff8d01c0ecdaa0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/ddb565cc-fa76-4246-9cf4-88d61b853eae.png?resizew=129)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e0c2455a9e796bba6861503f0fe31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f4aef2d294ce066c517691155cbb78.png)
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3卷引用:甘肃省武威市天祝藏族自治县第一中学2022-2023学年高一下学期第二次月考数学试题
3 . 梯形
中,
,
沿着
翻折,使点
到点
处,得到三棱锥
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f397c464b549e55b962a28ebd4cc991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f63756fe9251e65cc14e1ce9723d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
A.存在某个位置的点![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若平面![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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4 . 如图,60°的二面角的棱上有A、B两点,线段AC、BD分别在这个二面角的两个半平面内,且都垂直于AB,已知AB=4,AC=6,BD=8,则CD的长为
![](https://img.xkw.com/dksih/QBM/2019/1/21/2123405875363840/2123626014711808/STEM/6d41f61db1ef4ece94567d0d2658ca62.png?resizew=133)
![](https://img.xkw.com/dksih/QBM/2019/1/21/2123405875363840/2123626014711808/STEM/6d41f61db1ef4ece94567d0d2658ca62.png?resizew=133)
A.![]() | B.![]() | C.![]() | D.![]() |
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2018-01-19更新
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6卷引用:【全国百强校】甘肃省天水市第一中学2018-2019学年高二上学期期末考试数学(理)试题
名校
5 . 如图所示,已知二面角
的平面角为
,
,
,
、
为垂足,且
,
,设
、
到棱
的距离分别为
、
,当
变化时,点
的轨迹是下列图形中的( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/19/46654474-0375-4afb-bd22-26e02e34dc4d.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e35f3a470885d88519e1a71db4b323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4d7c644adf1763379806644b7729c3.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/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ce0586aafd9bf4fb7e1be082624afc.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/19/46654474-0375-4afb-bd22-26e02e34dc4d.png?resizew=167)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 如图所示,将等腰直角
沿斜边
上的高
折成一个二面角,使得
.那么这个二面角大小是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b99adaf772b59b1c6b4b23daa3c77a.png)
![](https://img.xkw.com/dksih/QBM/2021/1/19/2639503190532096/2667643775361024/STEM/eea7ef3d84ec4807ad88cd9e99435b73.png?resizew=141)
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4卷引用:甘肃省宁县第二中学2020-2021学年高一上学期期末数学试题
2012高二·甘肃天水·学业考试
真题
7 . 设P是
的二面角
内一点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5a95c17d2278aa48376746a7ef577f.png)
垂足,
则AB的长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11d0840c5718c42ce3fe43fa00a4755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5f0d07ad7876b56fc5c07337dfd6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5a95c17d2278aa48376746a7ef577f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e821d0efdae45834d3e4745bf9b6873a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5580effdcfc5afc3a228eb5d0099c1db.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2016-12-01更新
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3卷引用:2011-2012学年甘肃省天水一中高二第二次学业水平测试数学试卷
(已下线)2011-2012学年甘肃省天水一中高二第二次学业水平测试数学试卷山东省泰安第二中学2019-2020学年高三上学期10月月考数学试题2004 年普通高等学校招生考试数学(理)试题(重庆卷)