1 . 矩形
中,
(如图1),将
沿
折起到
的位置.点
在平面
上的射影
在
边上,连结
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/26c5c957-16b3-4c24-95c6-d66aabe75202.png?resizew=167)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/05123297-b8f3-44c2-8605-5895a384315f.png?resizew=203)
(1)证明:
;
(2)过直线
的平面
与
平行,求
与
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0ecba7e1969a265ff75bcb17ed9d2e.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/fb3d4de4f2a11ce4dd04c334e2680483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/26c5c957-16b3-4c24-95c6-d66aabe75202.png?resizew=167)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/10/05123297-b8f3-44c2-8605-5895a384315f.png?resizew=203)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d994a45f95ec665cc70801ed8134bcd0.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554b3b4c5ce7aca81becc07ed4903736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023·全国·模拟预测
名校
2 . 如图,在四棱锥
中,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/eedaa78a-a146-4087-bae0-537b1c77c7fa.png?resizew=158)
(1)证明:
.
(2)若
,点
到平面
的距离为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e198ba74cc4b55e69c48941acb01f0be.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/eedaa78a-a146-4087-bae0-537b1c77c7fa.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69d166677557cadb3da32b4a7e152e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02535e1a690ca111ca7a395a1bf48080.png)
您最近一年使用:0次
3 . 如图,边长为2的正方形ABCD所在的平面与半圆弧CD所在平面垂直,M是CD上异于C,D的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/3d9fca02-8214-448f-b6ac-df4eab901d81.png?resizew=185)
(1)证明:平面AMD⊥平面BMC;
(2)当三棱锥
体积最大时,求面MAB与面MCD所成二面角的正切值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/27/3d9fca02-8214-448f-b6ac-df4eab901d81.png?resizew=185)
(1)证明:平面AMD⊥平面BMC;
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
您最近一年使用:0次
2023-03-25更新
|
587次组卷
|
4卷引用:贵州省凯里市第一中学2022-2023学年高二下学期第一次月考数学试题
贵州省凯里市第一中学2022-2023学年高二下学期第一次月考数学试题四川省绵阳市南山中学2022-2023学年高二下学期期中考试数学(理)试题湖南省岳阳市平江县颐华高级中学2023-2024学年高三上学期入学考试数学试题(已下线)第6章 空间向量与立体几何 单元测试(B卷重难过关)-【学霸满分】2022-2023学年高二数学下学期重难点专题提优训练(苏教版2019选择性必修第二册)
名校
解题方法
4 . 如图甲,在四边形
中,
,
,将
沿
折起得图乙,点
是
上的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/6ebc80a6-0f13-472d-90e4-8cf7e7e81ff6.png?resizew=313)
(1)若
为
的中点,证明:
平面
;
(2)若
,试确定
的位置,使二面角
的正弦值等于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864c21e9664fa9111ede6425b09563a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3185a8075eea774ea1c6298fd1d0f5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32f7d17decde7a4c9d066dc9d648530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/6ebc80a6-0f13-472d-90e4-8cf7e7e81ff6.png?resizew=313)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3e27f6e6d1592408508cc9fd14d480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e9ac46aabe38e5ea1a8cb0febc98af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
您最近一年使用:0次
2023-03-23更新
|
1487次组卷
|
3卷引用:贵州省2023届高三3+3+3高考备考诊断性联考(二)数学(理)试题
解题方法
5 . 如图甲,在四边形PBCD中,
,
.现将△ABP沿AB折起得图乙,点M是PD的中点.证明:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/8ba02e43-77b6-4d54-8539-207f38edc08b.png?resizew=388)
(1)
;
(2)PC⊥平面ABM.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325d8bf47ff0aac5e0b1d55be34112e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b4c985fd9564f78c651fb597634e3c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/8ba02e43-77b6-4d54-8539-207f38edc08b.png?resizew=388)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e4b16c2c6c9bd089da78122e9d2511.png)
(2)PC⊥平面ABM.
您最近一年使用:0次
6 . 正方体
中,AC与BD交于点O,点E,F分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/95472ad1-e8d7-4568-bb71-dcd9604aae07.png?resizew=194)
(1)求证:平面
平面BEO;
(2)若正方体的棱长为2,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e86e3991200297ad172455e5ea93f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/95472ad1-e8d7-4568-bb71-dcd9604aae07.png?resizew=194)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9bbbb23bd5e1cbe61408bd632350f3.png)
(2)若正方体的棱长为2,求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e80318b27b799587e8771a6b6270dbd1.png)
您最近一年使用:0次
2023-03-21更新
|
532次组卷
|
4卷引用:贵州省毕节市2023届高三诊断性考试(二)数学(文)试题
贵州省毕节市2023届高三诊断性考试(二)数学(文)试题(已下线)专题13 押全国卷(文科)第18题 立体几何(已下线)专题13立体几何(解答题)宁夏回族自治区石嘴山市第三中学2023届高三第四次模拟考试数学(文)试题
7 . 如图,在直三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/cf51c86b-aa43-4c78-a136-33d2efdf667b.jpg?resizew=169)
(1)试在平面
内确定一点H,使得
平面
,并写出证明过程;
(2)若平面
与底面
所成的锐二面角为60°,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/cf51c86b-aa43-4c78-a136-33d2efdf667b.jpg?resizew=169)
(1)试在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62932e03d3081539626dced0530ad1ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
您最近一年使用:0次
解题方法
8 . 在棱长为6的正方体
中,E为
的中点,P在棱BC上(不包括端点),则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.存在点P,使得AP⊥平面![]() |
B.存在点P,使得三棱锥![]() |
C.存在点P,使得点P到DE的距离为5 |
D.当P为BC的中点时,三棱锥![]() |
您最近一年使用:0次
2023-03-17更新
|
1043次组卷
|
3卷引用:贵州省遵义市第十八中学2022-2023学年高二下学期第一次月考数学试题
名校
9 . 如图甲,已知四边形
是直角梯形,
,
分别为线段
,
上的点,且满足
,
,
,
,将四边形
沿
翻折,使得
,
分别到
,
的位置,并且
,如图乙
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/073c96bf-b74e-4bcb-9669-31ed030adddb.png?resizew=308)
(1)求证:
;
(2)求平面
与平面
所成的二面角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c75d8581bb7b2a91795852acdc07d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dda460b3099274f7ec63376b035c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d35d8d8bb0dc17f2f86fe5b230a2b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb79e86ac3a8a4f97e760e2dec04ad8d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/15/073c96bf-b74e-4bcb-9669-31ed030adddb.png?resizew=308)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21460a8145ad1b2c22eb6d42d706a43e.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ba1f8922a40840d56b1e9b3ae72a5b.png)
您最近一年使用:0次
2023-03-14更新
|
358次组卷
|
2卷引用:贵州省六校联盟2023届高三下学期适应性考试(三)数学(理)试题
10 . 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)
您最近一年使用:0次
2023-03-14更新
|
759次组卷
|
12卷引用: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
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)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