名校
解题方法
1 . 如图,四边形
是菱形,且
,P是平面
外一点,
为正三角形,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962141999013888/2962853384200192/STEM/88010877-c028-4fc9-9554-52a4d1657025.png?resizew=180)
(1)若G为边
的中点,求证:
平面
;
(2)若E为边BC的中点,能否在边PC上找出一点F,使平面
平面
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962141999013888/2962853384200192/STEM/88010877-c028-4fc9-9554-52a4d1657025.png?resizew=180)
(1)若G为边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf65b8884909d735d575efe81a2d2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若E为边BC的中点,能否在边PC上找出一点F,使平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6dd051db98c531f9ef18cdfd793f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-04-21更新
|
2332次组卷
|
4卷引用:第8章立体几何初步(基础、典型、易错、压轴)分类专项训练
(已下线)第8章立体几何初步(基础、典型、易错、压轴)分类专项训练沪教版(2020) 必修第三册 达标检测 第10章 10.4 平面与平面的位置关系河南省濮阳市第一高级中学2021-2022学年高一下学期期中理科数学试题江西省景德镇一中2021-2022学年高一(19班)下学期期末考数学试题
名校
2 . 在圆锥PO中,高
,母线
,B为底面圆O上异于A的任意一点.
![](https://img.xkw.com/dksih/QBM/2022/4/14/2958094116044800/2959245912768512/STEM/910e6a9c-8820-46c4-b2b2-9fcbf48d850f.png?resizew=389)
(1)当
时,过底面圆心O作
所在平面的垂线,垂足为H,求证:
;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://img.xkw.com/dksih/QBM/2022/4/14/2958094116044800/2959245912768512/STEM/910e6a9c-8820-46c4-b2b2-9fcbf48d850f.png?resizew=389)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25490c72ad1b9968e6be5c5f6b268ab3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d162c29b1e484cfc87350dd68f00b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb92d6ab1b9a520e272f3649f35ab07a.png)
您最近一年使用:0次
2022-04-16更新
|
1832次组卷
|
5卷引用:秘籍06 空间向量与立体几何(理)-备战2022年高考数学抢分秘籍(全国通用)
(已下线)秘籍06 空间向量与立体几何(理)-备战2022年高考数学抢分秘籍(全国通用)(已下线)回归教材重难点03 空间向量与立体几何-【查漏补缺】2022年高考数学(理)三轮冲刺过关甘肃省2022届高三第二次高考诊断考试数学(理)试题吉林省白山市抚松县第一中学2023届高考模拟预测数学试题宁夏回族自治区固原市西吉中学2024届高三上学期第五次模拟考试数学(理)试题
名校
3 . 如图,四边形
是正方形,
平面
,
,
,
,F为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/10/2933351405576192/2938037186764800/STEM/ea88ee5151bd4014a6200ea5a6021887.png?resizew=174)
(1)求证:
平面
;
(2)求二面角
的大小.
![](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/85ff59abe5e0a0f35141a78e63da7579.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82465b63174087aeba7788ed984583d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07dd741bc3f02d8552afbcf63fba4fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2022/3/10/2933351405576192/2938037186764800/STEM/ea88ee5151bd4014a6200ea5a6021887.png?resizew=174)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f306ff6d237cd9d847aa109acf9333d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729a3ac9d8a312996c1aa9eb2e1959fa.png)
您最近一年使用:0次
2022-03-17更新
|
2684次组卷
|
6卷引用:秘籍06 空间向量与立体几何(理)-备战2022年高考数学抢分秘籍(全国通用)
4 . 如图所示,在等腰梯形
中,
,在等腰梯形
中,
,将等腰梯形
沿
所在直线翻折,使得E,F在平面
上的射影恰好与A,B重合.
![](https://img.xkw.com/dksih/QBM/2022/1/23/2901515314233344/2909373355532288/STEM/62185e876d1c45a08bf64d42c5885951.png?resizew=553)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/873d7c7185a904b8ed550902ec1f5820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725aa3cd046b43f38926fc7c595d9046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2022/1/23/2901515314233344/2909373355532288/STEM/62185e876d1c45a08bf64d42c5885951.png?resizew=553)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
名校
5 . 如图,在四棱台
中,底面
为矩形,平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/dedd57f5-edc7-4b86-8150-ba5e12922bbc.png?resizew=172)
(1)求证:
;
(2)求直线
和平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384ffa4e596b6c7b8e270217a47f7227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6503add5811927fc11d86f2174f79f1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/dedd57f5-edc7-4b86-8150-ba5e12922bbc.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e076e68ef7bab94a6aba990f83159f51.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2022-02-04更新
|
1520次组卷
|
3卷引用:技巧03 解答题解法与技巧(练)--第二篇 解题技巧篇-《2022年高考数学二轮复习讲练测(浙江专用)》
(已下线)技巧03 解答题解法与技巧(练)--第二篇 解题技巧篇-《2022年高考数学二轮复习讲练测(浙江专用)》浙江省绍兴市2021-2022学年高三上学期期末数学试题上海市实验学校2024届高三上学期暑假阶段反馈数学试题
6 . 在三棱锥
中,
,
,
两两互相垂直,E为
的中点,且
,求直线AE与BC所成角的大小(用两种方法解答).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef9de8db4d3ad85abdfb5d854082acb.png)
您最近一年使用:0次
2022-01-17更新
|
825次组卷
|
4卷引用:模块三 专题7 大题分类练(立体几何初步)基础夯实练(人教A)
(已下线)模块三 专题7 大题分类练(立体几何初步)基础夯实练(人教A)(已下线)模块三 专题8(立体几何初步)基础夯实练(北师大版)辽宁省大连市2021-2022学年高二上学期期末数学试题人教B版(2019)选择性必修第一册课本例题1.2.1 空间中的点、直线与空间向量
7 . 在空间几何体
中,
平面
,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/9/2890852519501824/2893539641008128/STEM/6e265923-9fb9-4e59-b383-67fbd7e8f240.png?resizew=166)
(1)求证:
平面
;
(2)若
平面
,试比较三棱锥
与
的体积的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8a3ffc690e57df945f132e9bffd085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf7c14f4ecf33ee9938a76c3ac45d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b12b6d1e4fc6fce56bf1bd6d4e41ae1.png)
![](https://img.xkw.com/dksih/QBM/2022/1/9/2890852519501824/2893539641008128/STEM/6e265923-9fb9-4e59-b383-67fbd7e8f240.png?resizew=166)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee188333e1fa99417aede565c6a4a136.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee188333e1fa99417aede565c6a4a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c61c958e98e615a532efaa67d48c3de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2022高三·全国·专题练习
8 . 如图,已知平面
与直线
均垂直于
所在平面,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/5cadd582-9bd2-46d1-b58c-d19122cdfa19.png?resizew=159)
(1)求证:
平面
;
(2)若
平面
,求二面角
的钝二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee188333e1fa99417aede565c6a4a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7281b641656a5992abaafb4190ca9afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad01edc5d969ef89c350b5614c386db9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/5cadd582-9bd2-46d1-b58c-d19122cdfa19.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee188333e1fa99417aede565c6a4a136.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee188333e1fa99417aede565c6a4a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44002ba2148c32bacdab4c0a498ffd4a.png)
您最近一年使用:0次
20-21高一·全国·课后作业
9 . 如图,在三棱锥
中,
分别是
的中点,点
在
上,点
在
上,且有
.试判定直线
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0058f338cafb4ea78d40f5de280d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a07c9674387af7bd0f4d5044a0b871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4967c1c767e344de1ddb9c07608ee3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd733c4abe9c3536366ad22efd4c5089.png)
您最近一年使用:0次
2021-11-13更新
|
571次组卷
|
7卷引用:8.4 空间点、直线、平面之间的位置关系(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)
(已下线)8.4 空间点、直线、平面之间的位置关系(精练)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)(已下线)第一章 点线面位置关系 专题三 共点问题 微点1 立体几何共点问题的解法【基础版】(已下线)第十三章本章回顾(已下线)第15讲 空间点、直线、平面之间的位置关系-【寒假自学课】2022年高一数学寒假精品课(人教A版2019必修第二册)(已下线)8.4 空间点、直线、平面之间的位置关系陕西省榆林市定边县第四中学2022-2023学年高一下学期期中数学试题苏教版(2019)必修第二册课本习题第13章复习题
名校
10 . 如图,直四棱柱
的底面
是平行四边形,
,
,
,点
是
的中点,点
在
且
.
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844863191736320/2849768661663744/STEM/62d467d7444646de9f5ca0bde29f4346.png?resizew=265)
(1)证明:
平面
;
(2)求锐二面角
平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4cb73e9d976cbfe9c590044fa69dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c3ec174b1ce835cc8737ff6ce57e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4272ca39f8f4d12bcbc4a0bc50e8f001.png)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844863191736320/2849768661663744/STEM/62d467d7444646de9f5ca0bde29f4346.png?resizew=265)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6238a6fb52a9d2e3521ba66ef9a5c247.png)
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