1 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/2fbd0e73faf147d98a44dedba9a207e7.png)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)在棱
上是否存在点
,使得
平面
?若存在,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958330f56d75b05fbf9144e6fd458be4.png)
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/2fbd0e73faf147d98a44dedba9a207e7.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/d0dd839ad128404c9301c9dd17007ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da035673ef0edcfae6b72fb5e5ba34a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(3)在棱
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/79c6d89dfb664e5c8e4da378f97be95d.png)
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/b0d6af4a30bf4905bd5f25ccbdfff341.png)
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/6bfa3fbaf95043bfa8fc7ba5360a0581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/2016/6/13/1572740890648576/1572740896784384/STEM/eb7c30b9cad047a3a45fdaac5be8291b.png)
您最近一年使用:0次
2016-12-04更新
|
270次组卷
|
42卷引用:2020届北京市陈经纶学校高三上学期数学10月份月考试卷
2020届北京市陈经纶学校高三上学期数学10月份月考试卷2016年全国普通高等学校招生统一考试理科数学(北京卷精编版)2017届四川绵阳中学高三上学期入学考试数学(理)试卷2016-2017学年湖北省武汉市第二中学高二上学期期末考试数学(理)试卷天津市实验中学2017-2018学年高二上学期期中考试数学(理)试题人教A版高中数学 高三二轮 专题05 立体几何中的空间角问题 测试北京市2019届高三数学理一轮复习典型题专项训练:立体几何2020届天津市南开中学高三上学期数学统练九试题天津市耀华中学2018-2019学年高三(下)开学考数学试题(理科)(已下线)专题17 立体几何综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题17 立体几何综合-五年(2016-2020)高考数学(理)真题分项浙江省金华市东阳中学2020-2021学年高二上学期10月段考数学试题(已下线)第08章 立体几何(单元检测)-2021届高考数学(理)一轮复习讲练测(已下线)期末测试(选择性必修一+必修二)(能力提升)-2020-2021学年高二数学单元测试定心卷(人教B版2019选择性必修第二册)(已下线)专题09 立体几何(讲)-2021年高考数学二轮复习讲练测(文理通用)(理科)(已下线)理科数学-2021年高考数学押题预测卷(新课标Ⅱ卷)02(已下线)【新东方】双师291高一下(已下线)上海市华东师范大学第二附属中学2021届高三下学期三月月考数学试题安徽省巢湖市黄山中学2019-2020学年高二上学期第一次月考文科数学试题黑龙江省农垦宝泉岭高级中学2021-2022学年度高二学年上学期第一次月考数学试题(已下线)专题26空间向量与空间角的计算-2022年高三毕业班数学常考点归纳与变式演练(理科专用)广东省揭阳市普宁市华侨中学2021-2022学年高二上学期期中数学试题北京市第十三中学2022届高三12月月考数学试题(已下线)第八章 立体几何初步 章末测试(提升)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)山西省太原师范学院附属中学、太原市师苑中学校2021-2022学年高一下学期第四次联考数学试题湖北省随州市曾都区第一中学2022-2023学年高二上学期开学测试数学试题北京市东直门中学2021-2022学年高二上学期期中数学试题山东省青岛超银高级中学2022-2023学年高二上学期10月月考数学试题四川省雅安市芦山县芦山中学2020-2021学年高二下学期期中数学理科试题河南省鹤壁市高中2022-2023学年高二上学期10月月考数学试题河南省信阳高级中学2022-2023学年高二上学期10月巩固测试数学试题(已下线)2016年全国普通高等学校招生统一考试理科数学(北京卷参考版)(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项北京十年真题专题07立体几何与空间向量陕西省渭南市富平中学2024届高三上学期开学摸底考试理科数学试题北京市第六十五中学2023—2024学年高二上学期期中考试数学试题(已下线)第五章 破解立体几何开放探究问题 专题一 立体几何存在性问题 微点3 立体几何存在性问题的解法综合训练【基础版】(已下线)第五章 破解立体几何开放探究问题 专题一 立体几何存在性问题 微点1 立体几何存在性问题的解法(一)【基础版】辽宁省朝阳市建平县实验中学2023-2024学年高二下学期3月月考数学试题(已下线)专题23 立体几何解答题(理科)-3(已下线)【一题多解】存在与否 向量探索专题09立体几何与空间向量(第二部分)
名校
解题方法
2 . 如图,在四棱锥
中,底面
是正方形,侧面
底面
,
,点
是
的中点,点
在边
上移动.
![](https://img.xkw.com/dksih/QBM/2015/3/18/1572013575946240/1572013581713408/STEM/4382da8ba42e40c5a1fd771e668a666f.png?resizew=206)
(1)若
为
中点,求证:
//平面
;
(2)求证:
;
(3)若
,二面角
的余弦值等于
,试判断点
在边
上的位置,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2015/3/18/1572013575946240/1572013581713408/STEM/4382da8ba42e40c5a1fd771e668a666f.png?resizew=206)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c95b6b6e8fd9fc8e8084b5706b4b48.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74107ed86d62c4a2ca1630d626dff115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5f8dfb22b415219ba7af3dc7e3d808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743c08870d66a766fa25298adf4dbf89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2016-12-03更新
|
1683次组卷
|
2卷引用:2015届北京市朝阳区高三上学期期末考试理科数学试卷
12-13高三上·北京朝阳·期末
解题方法
3 . 如图,在四棱锥
中,平面
平面
.底面
为矩形,
,
.
(1)求证:
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1708dc73d3e9d8d15f64678c785c59de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cac3dd1a52c27975c6c04819cb3b96a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0d3228717a954dd5be8f9585833c13.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b787fcc1da13b8665a7d6a41a75328.png)
![](https://img.xkw.com/dksih/QBM/2012/1/16/1570693360885760/1570693366325248/STEM/1a587af2-3eba-40a6-b072-26c823f17bc9.png?resizew=180)
您最近一年使用:0次
4 . 已知四边形
为直角梯形,
,
,
,
,
为
中点,
,
与
交于点
,沿
将四边形
折起,连接
.
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647224830664704/1652846661083136/STEM/78eeea4cd1fd4b5a9f4c398ed47612de.png?resizew=432)
(1)求证:
平面
;
(2)若平面
平面
.
(I)求二面角
的平面角的大小;
(II)线段
上是否存在点
,使
平面
,若存在,求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1391573c30964b87ca3429bf67ae22aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41c2d7ae6aaf6d91129ed5221a415a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe579fdac91d16b1161fff5ce47c422.png)
![](https://img.xkw.com/dksih/QBM/2017/3/19/1647224830664704/1652846661083136/STEM/78eeea4cd1fd4b5a9f4c398ed47612de.png?resizew=432)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5628323a7eeb11213df5c9048b3543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41c2d7ae6aaf6d91129ed5221a415a7.png)
(I)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
(II)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc93b583624ebda8d0237437c22ca262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbda5eb3f3becbc98276be833ccbe29f.png)
您最近一年使用:0次
2017-03-27更新
|
1280次组卷
|
2卷引用:北京市朝阳区2019~2020学年高三上学期抽样检测数学试题
11-12高三下·北京朝阳·阶段练习
名校
5 . 在如图所示的几何体中,四边形
为平行四边形,
,
平面
,
,
,
,且
是
的中点.
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的大小;
(Ⅲ)在线段
上是否存在一点
,使得
与
所成的角为
? 若存在,求出
的长度;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d7b8c8a8aaff1053b0677cdd3539d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45d1180cb19d139a950b27306035a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac4401d39079cc4284b1d5977b8c922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71337caec78cbfb07b7501e8ccc92a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c4f8bd9f03a28dc5ab676159930a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dceb5c62469c42bc018e2da4e7fbb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4bb9571b33d88f735fe6dc8fe41209.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b40bf08cb4c6a1d815882c13bd4216.png)
(Ⅲ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21002725043bdace95b3244d4c75dd74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcfaca9396f85c0137b534903321fcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff575e55857af133edb24c8e61504f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70a0eb6045369a13358f2d5999f7bc3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://img.xkw.com/dksih/QBM/2012/4/23/1570839413678080/1570839419084800/STEM/a9e4fe8df22e4261877676a8988cb63b.png?resizew=302)
您最近一年使用:0次