1 . 已知四边形
为平行四边形,
,
,
,四边形
为正方形,且平面
平面
.
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283871797248/1572283877982208/STEM/cc375cc5e2534c4ca70bff3c9f32ff4a.png)
(1)求证:
平面
;
(2)若
为
中点,证明:在线段
上存在点
,使得
∥平面
,并求出此时三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283871797248/1572283877982208/STEM/209ca889cf0d4e8ba70a3f244ed1be8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a1d4c140243ba9a9bd7256ec2bbce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283871797248/1572283877982208/STEM/23b1fd9d43a94a239d1608dc2925e04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283871797248/1572283877982208/STEM/cc375cc5e2534c4ca70bff3c9f32ff4a.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283871797248/1572283877982208/STEM/d55f968f2c3046039285b9644b0528a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa3254460ecbacecb3e57c5dce227f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f511c0a9759d9b3d2adbf884a14ca52.png)
您最近一年使用:0次
2 . 一个长方体的平面展开图及该长方体的直观图的示意图如图所示.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
标记在长方体相应的顶点处(不需说明理由);
(2)在长方体中,判断直线
与平面
的位置关系,并证明你的结论;
(3)在长方体中,设
的中点为
,且
,
,求证:
平面
.
![](https://img.xkw.com/dksih/QBM/2017/1/17/1619458715213824/1619458715779072/STEM/97ab1bd717c7490c9a6ba5a6e9d88423.png)
(1)请将字母
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
(2)在长方体中,判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a8898c347a62c7de2bdca3f3c7e33.png)
(3)在长方体中,设
![](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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c6c83ab4abc895ac36ab888a55be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53569e6ec795658b4fffcddeebe0f142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73153657848013d2a1c3247d7f84ddeb.png)
您最近一年使用:0次
3 . 在直三棱柱ABC﹣A1B1C1中,BC=CC1,AB⊥BC.点M,N分别是CC1,B1C的中点,G是棱AB上的动点.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287347712/STEM/af60347b036b43508ebf6a5d8329bcd1.png)
(Ⅰ)求证:B1C⊥平面BNG;
(Ⅱ)若CG∥平面AB1M,试确定G点的位置,并给出证明.
![](https://img.xkw.com/dksih/QBM/2016/1/22/1572462281269248/1572462287347712/STEM/af60347b036b43508ebf6a5d8329bcd1.png)
(Ⅰ)求证:B1C⊥平面BNG;
(Ⅱ)若CG∥平面AB1M,试确定G点的位置,并给出证明.
您最近一年使用:0次
名校
解题方法
4 . 如图,在三棱柱
中,
平面
,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/c79735a0-9659-4d9d-9ea7-c15604eec8b9.png?resizew=144)
(1)求证:
;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe312c442d13f937a286c0ed069d6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61ef77be3243e46e5591c4bc4c99942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/6655cc150ddc9deba2254780984d0024.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/c79735a0-9659-4d9d-9ea7-c15604eec8b9.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b500528c1f0ed3a48e63a44788b9956.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
您最近一年使用:0次
2022-10-29更新
|
404次组卷
|
4卷引用:宁夏银川市银川六中2019-2020学年高二上学期期末考试试题
名校
解题方法
5 . 如图,四棱锥
的底面是边长为a正方形,每条侧棱长都是底面边长的
倍,P为侧棱SD上的点.
![](https://img.xkw.com/dksih/QBM/2022/5/15/2979504463380480/2981509862113280/STEM/ae5fee007ccb4d81881e29449c9bae47.png?resizew=191)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c177e06cc3f703e8ca7be7c491fa2942.png)
(2)若
,侧棱SC上是否存在一点E,使得
,若存在,求
的值,若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/15/2979504463380480/2981509862113280/STEM/ae5fee007ccb4d81881e29449c9bae47.png?resizew=191)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c177e06cc3f703e8ca7be7c491fa2942.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb446da7614cc62fd0f5c041ae403807.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e58abb2fa685b7dfe6ca8fbb3543ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9013fec36586592a57b9abfb6ce4ffa.png)
您最近一年使用:0次
2022-05-17更新
|
620次组卷
|
6卷引用:安徽省蚌埠市第二中学2019-2020学年高二上学期期中数学(文)试题
6 . 如图所示,在平行四边形
中,
,
,
,将△
沿
折起到△
的位置,使平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/3229f0c6-84bd-488c-8ebb-61de02aaa90f.png?resizew=149)
(Ⅰ)求证:
;
(Ⅱ)若点
为
的中点,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/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfaad4c4467e27421876d8f2a4371d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54cf75bbfc9db93d27937c8b8e977b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/3229f0c6-84bd-488c-8ebb-61de02aaa90f.png?resizew=149)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
(Ⅱ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
您最近一年使用:0次
2021-09-11更新
|
334次组卷
|
3卷引用:四川省眉山市2019-2020学年高二上学期期末考试数学(理)试题
名校
7 . 如图,已知三棱柱
,平面
平面
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/14/2699780907016192/2806720330907648/STEM/d81e3ded-334e-4162-8e92-a22d0d5e56ee.png?resizew=346)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a059ac387c0ba5972314f00063baa24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba5db30bb3d52a2781a8159ab1c76deb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82bc0ac36aa52b4d24c35789cc72672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba75ab97c8b4bb1f6cd7613d7532a5c3.png)
![](https://img.xkw.com/dksih/QBM/2021/4/14/2699780907016192/2806720330907648/STEM/d81e3ded-334e-4162-8e92-a22d0d5e56ee.png?resizew=346)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc90fee532e50d319081d571410421.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
2021-09-12更新
|
1185次组卷
|
8卷引用:广东省广州市执信中学2021届高三上学期第五次月考数学试题
名校
8 . 如图1,在平行四边形
中,
=60°,
,
,
,
分别为
,
的中点,现把平行四边形
沿
折起如图2所示,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b5d693c4f0c4d0e6c0c810e7d464b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6cb992b6faad4744f85d73a3b76dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c2b3adb41e8965f553da2e5086a751.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a677b42f8b427b21924a559b90141d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44507c93f6180afd1697d2fa5a5c741.png)
您最近一年使用:0次
2021-06-15更新
|
1645次组卷
|
12卷引用:2016届福建福州市高三上学期期末数学(理)试卷
2016届福建福州市高三上学期期末数学(理)试卷2017届河南南阳一中高三理上学期月考四数学试卷宁夏石嘴山市第三中学2017届高三下学期第三次模拟考试数学(理)试题河南省南阳市2018届高三期终质量评估数学(理)试题广西南宁二中2020届高三4月开学考试理数试题四川省成都市实验外国语学校2020届高三(高2017级)数学模拟(三)理试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)广东省广州市广州大学附属中学2021-2022学年高二上学期第一次月考数学试题广东省真光中学2021-2022学年高二上学期10月月考数学试题湖北省武汉一中2021届高三下学期二模数学试题(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)2023版 北师大版(2019) 选修第一册 突围者 第三章 专项拓展训练3 用空间向量解决折叠问题
名校
9 . 如图,E是以AB为直径的半圆O上异于A、B的点,矩形ABCD所在的平面垂直于半圆O所在的平面,且AB=2AD=2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/c5630bf6-3ebf-4962-8ebe-a03955b2ce04.png?resizew=145)
(1)求证:
;
(2)若异面直线AE和DC所成的角为
,求平面DCE与平面AEB所成的锐二面角的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/c5630bf6-3ebf-4962-8ebe-a03955b2ce04.png?resizew=145)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad2dc5dea4563dfd9afefeb8b210eeb.png)
(2)若异面直线AE和DC所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
您最近一年使用:0次
2020-07-02更新
|
1052次组卷
|
3卷引用:广东省2021届高三上学期新高考适应性测试(一)数学试题
广东省2021届高三上学期新高考适应性测试(一)数学试题福建省厦门市湖滨中学2020届高三下学期测试数学(理)试题(已下线)专题31 空间中直线、平面垂直位置关系的证明方法-学会解题之高三数学万能解题模板【2022版】
名校
10 . 如图,在三棱柱
中,侧面
是菱形,且
,平面
平面
,
,
,O为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/6/1/2475176207646720/2480894989836288/STEM/8f3c3b92-8326-4f15-9369-3e698aad4199.png?resizew=232)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1c28f4604d8b7baa8f17a042e8956f.png)
(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/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd57614136e2fc269f698a9c3904e31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37199965a41feed17c44f208b029945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2879880d7d25341a07729b6dd598e4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/2020/6/1/2475176207646720/2480894989836288/STEM/8f3c3b92-8326-4f15-9369-3e698aad4199.png?resizew=232)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1c28f4604d8b7baa8f17a042e8956f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74262b3b5ef44a90e51e1d2c94436a97.png)
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2020-06-09更新
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161次组卷
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3卷引用:广东省阳春市第一中学2019-2020学年高二下学期月考四数学试题