1 . 在如图所示的几何体中,正方形
与梯形
所在平面相交,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/1e3705cf-bc51-44b3-9be2-f4544ea1df1c.png?resizew=175)
(1)证明:
平面
;
(2)若
平面
,试求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d525d8b43670233010b604ddf383b4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c56903f8f497bc868ef67bd3d8593d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/1e3705cf-bc51-44b3-9be2-f4544ea1df1c.png?resizew=175)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
您最近一年使用:0次
解题方法
2 . 如图,在多面体
中,四边形
是直角梯形,
,
,
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/beaac8de-694f-4795-ade3-366852fe4428.png?resizew=158)
(1)证明:
平面
.
(2)若
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed619e2dc900c52a29012e5b821451bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b28bf7a1162221c19758f421f012650.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/beaac8de-694f-4795-ade3-366852fe4428.png?resizew=158)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75aea24647cd4d0b4b9aa513bf5457b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8fe122a768a4d78b5b39817d557a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
您最近一年使用:0次
解题方法
3 . 如图,正方形
为圆柱
的轴截面,
是圆柱上异于
的母线,
分别是
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/6f0da5d2-3b53-4efc-90fb-517dd3320b8f.png?resizew=143)
(1)证明:
平面
;
(2)设平面
与圆
所在平面的交线为
,证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d93949d8a15aca4e79cedb978590571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19097651607095bc2bf9298bb964c392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1b4436b6671342685977ac740c0e1f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/6f0da5d2-3b53-4efc-90fb-517dd3320b8f.png?resizew=143)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea3f72e0891faef8395825fb7847d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23976db53f05b3d5d791c4d736a7184d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
2022-04-25更新
|
859次组卷
|
4卷引用:河南省洛阳市2021-2022学年高一下学期期中数学试题
河南省洛阳市2021-2022学年高一下学期期中数学试题(已下线)13.2.4平面与平面位置关系(1)平面与平面平行的判定与性质(备作业)-【上好课】2021-2022学年高一数学同步备课系列(苏教版2019必修第二册)2023版 湘教版(2019) 必修第二册 过关斩将 第4章 4.3 直线与直线、直线与平面的位置关系 4.3.2 空间中直线与平面的位置关系 第1课时 直线与平面平行(已下线)8.5空间直线、平面的平行——课后作业(巩固版)
名校
4 . 如图,三棱柱
中侧棱与底面垂直,且
,
,
,M,N,P,D分别为
,BC,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/83254c6e-4fd1-49a1-84d0-f549b8705b78.png?resizew=220)
(1)求证:
面
;
(2)求平面PMN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/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/83254c6e-4fd1-49a1-84d0-f549b8705b78.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc027de6ca8c118ed6ccd52eae99a821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求平面PMN与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2022-06-05更新
|
1843次组卷
|
6卷引用:四川省成都市蓉城高中教育联盟2021-2022学年高二下学期期中考试理科数学试题
四川省成都市蓉城高中教育联盟2021-2022学年高二下学期期中考试理科数学试题河北省石家庄市第二中学2022届高三下学期高考考前模拟数学试题(已下线)2022年全国新高考II卷数学试题变式题13-16题江苏省镇江第一中学2021-2022学年高二下学期期末数学试题(已下线)2022年全国新高考II卷数学试题变式题20-22题辽宁省沈阳市东北育才学校科学高中部2021-2022学年高三下学期最后一次模拟数学试题
名校
5 . 在如图所示的圆柱
中,
为圆
的直径,
、
是
的两个三等分点,
、
、
都是圆柱
的母线.
![](https://img.xkw.com/dksih/QBM/2022/4/24/2965187534807040/2998300579651584/STEM/53fbef0c3f8a49049af2c1e36848a21c.png?resizew=175)
(1)求证:
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.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/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4083c581c6027c4b2ae7e3b3749f485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://img.xkw.com/dksih/QBM/2022/4/24/2965187534807040/2998300579651584/STEM/53fbef0c3f8a49049af2c1e36848a21c.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d8662513d307ed16683319e997494d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797835e3ba47ab72406d50249adeb593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a38a3e226347af68d7b15295342e209.png)
您最近一年使用:0次
2022-06-10更新
|
1274次组卷
|
12卷引用:山东师范大学附属中学2021-2022学年高三下学期4月线上测试数学试题
山东师范大学附属中学2021-2022学年高三下学期4月线上测试数学试题湖南省永州市2021届高三下学期二模数学试题(已下线)专题37 仿真模拟卷03-2021年高考数学(理)二轮复习热点题型精选精练(已下线)精做04 立体几何-备战2021年高考数学大题精做(新高考专用)(已下线)专题1.7 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)江苏省徐州市2021届高三下学期第三次调研测试数学试题西藏自治区拉萨中学2021届高三第八次月考数学(理)试题四川省成都市石室中学2021届高三三模模拟考试数学试题(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)1.2.4 二面角(已下线)2022年全国新高考II卷数学试题变式题20-22题新疆巴音郭楞蒙古自治州若羌县中学2022-2023学年高二下学期3月月考数学试题
名校
6 . 已知底面ABCD为菱形的直四棱柱,被平面AEFG所截几何体如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/594b9562-51ce-470a-90d9-8686b0d06bec.png?resizew=232)
(1)若
,求证:
;
(2)若
,
,三棱锥GACD的体积为
,直线AF与底面ABCD所成角的正切值为
,求锐二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/594b9562-51ce-470a-90d9-8686b0d06bec.png?resizew=232)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4da6d55f36613f4c677d479358fce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a67d05f2f5e3e6fd43fb60e8c53d4f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f4f259d60ade01bd9bf6632238e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b98d08cb05a894f940009f56c74d83c.png)
您最近一年使用:0次
2022-06-07更新
|
1708次组卷
|
4卷引用:广东省广外、广附、铁一三校2022-2023学年高二上学期期中联考数学试题
解题方法
7 . 如图,在正方体
中,
是
的中点,
,
,
分别是
,
,
的中点,求证:
![](https://img.xkw.com/dksih/QBM/2022/5/8/2974933547376640/2979080373813248/STEM/e0efe439-5142-4d5a-b7ac-d28a804ac5a0.png?resizew=200)
(1)直线
平面
;
(2)
为线段
上一点,且
,求证:
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/8/2974933547376640/2979080373813248/STEM/e0efe439-5142-4d5a-b7ac-d28a804ac5a0.png?resizew=200)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31d54d125c042169e282f14eddd45a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f9d6c4583b60e2ece705889264f0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e82b3e225741b7f541fb6cff225d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
2022-05-14更新
|
1496次组卷
|
6卷引用:广东省深圳实验学校2021-2022学年高一下学期期中数学试题
广东省深圳实验学校2021-2022学年高一下学期期中数学试题广东省惠州一中、珠海一中、中山纪念中学2021-2022学年高一下学期第二次段考数学试题(已下线)第11练 空间直线、平面的平行-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)(已下线)空间直线、平面的平行(已下线)专题08 空间直线与平面的平行问题(1)-期中期末考点大串讲广东省2024年普通高中学业水平合格性考试考前冲刺数学试题二
名校
8 . 如图,AP是圆柱的母线,正△ABC是该圆柱的下底面的内接三角形,D,E,F分别为BC,PB,AB的中点,G是EF的中点,且AP=AC.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854639979487232/2858441973432320/STEM/c4c74883-a062-4fd1-9673-0b9c6354a888.png)
(1)求证:DG
平面PAC;
(2)求直线DG与平面PBC所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854639979487232/2858441973432320/STEM/c4c74883-a062-4fd1-9673-0b9c6354a888.png)
(1)求证:DG
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
(2)求直线DG与平面PBC所成角的正弦值.
您最近一年使用:0次
2021-11-24更新
|
276次组卷
|
3卷引用:山东省潍坊市昌邑市潍坊实验中学2023-2024学年高二上学期数学期中模拟卷(一)
名校
9 . 如图,三棱柱
中侧棱与底面垂直,且AB=AC=2,AA1=4,AB⊥AC,M,N,P,D分别为CC1,BC,AB,
的中点.
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
您最近一年使用:0次
10 . 如图所示,在直三棱柱
中,
,
,点
分别为棱
,
的中点,点
是线段
上的点(不包括两个端点).
![](https://img.xkw.com/dksih/QBM/2022/5/1/2969888881025024/2970026896293888/STEM/689068d4a96b4032aae751b60c8a04f9.png?resizew=212)
(1)设平面
与平面ABC相交于直线m, 求证:
;
(2)当
为线段
的中点时,求点
到平面
的距离;
(3)是否存在一点
,使得二面角
的余弦值为
,如果存在,求出
的值;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96a6b20a35af7755e5d90789ea862da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/1/2969888881025024/2970026896293888/STEM/689068d4a96b4032aae751b60c8a04f9.png?resizew=212)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5462d242e01ea2c26c1f31aeccf27a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(3)是否存在一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3793f8863ff929602e3e60ebae6127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d0f451005f07f21f3380c707dc79d4.png)
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