名校
解题方法
1 . 如图,四边形
与
均为菱形,
,
,
,记平面
与平面
的交线为
.
;
(2)证明:平面
平面
;
(3)记平面
与平面
夹角为
,若正实数
,
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf80b036459da6dcb841a4bbe3859fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d223346f234798b92bd1eaa78360b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7ce5d5cc777ef4d5b890cc9cbb70b0.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b6711e6dd48be6cf8fa52926924d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b7195a853621ea5bebe8d2d1436732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b992104248a854e6e033c26602aff813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bfbdbf0f1957459f12ae149d5176e.png)
您最近一年使用:0次
2023-07-11更新
|
1849次组卷
|
5卷引用:四川省成都外国语学校2023-2024学年高二上学期10月月考数学试题
名校
2 . 如图,在正三棱柱
中,
,
为
的中点,
、
在
上,
.
(1)试在直线
上确定点
,使得对于
上任一点
,恒有
平面
;(用文字描述点
位置的确定过程,并在图形上体现,但不要求写出证明过程)
(2)已知
在直线
上,满足对于
上任一点
,恒有
平面
,
为(1)中确定的点,试求当
的面积最大时,二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa40b456747f69437444833aab387be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.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/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2564f406fa222935e6d5bb24df0356a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/c34c1d0d-b0de-4ab5-8ff6-a1140bfc6c2c.png?resizew=127)
(1)试在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826bf6fa3706921b77ad0eb4fcc206bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de8026bd1b6af298df08e532c2847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b17d7abbd564ce785f43a7c8526dc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef68c72248af27e3b83b4ee5fdeb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6b513ee7d966df71cd98b29ca4447e.png)
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2023-07-09更新
|
816次组卷
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6卷引用:10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)
(已下线)10.4 平面与平面间的位置关系(第2课时)(九大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题04 立体几何初步(2)-【常考压轴题】(已下线)第二章 立体几何中的计算 专题一 空间角 微点10 二面角大小的计算综合训练【培优版】福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题福建省永春第一中学2023-2024学年高一上学期8月月考数学试题福建省厦门市第一中学2023-2024学年高二上学期开学考试数学试题
名校
解题方法
3 . 如图,在三棱柱
中,平面
平面
,侧面
是边长为2的正方形,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/44e29202-58ce-4e59-a9ae-6b55a7711348.png?resizew=199)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0d0e78101fef36a75b70ac7e7cf5b.png)
(2)请再从下列三个条件中选择一个补充在题干中,完成题目所给的问题.
①直线
与平面
所成角的大小为
;②三棱锥
的体积为
;③
. 若选择条件___________.
求(i)求二面角
的余弦值;
(ii)求直线
与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ba5715a95b8de18c637c12c3d30d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0d0e78101fef36a75b70ac7e7cf5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12b92bb195943c794a3b3cf135d71a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddef39ef9ed3da136c4ed8b5d28b73e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/44e29202-58ce-4e59-a9ae-6b55a7711348.png?resizew=199)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0d0e78101fef36a75b70ac7e7cf5b.png)
(2)请再从下列三个条件中选择一个补充在题干中,完成题目所给的问题.
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da67af246912670bac6dc860f301383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4fcf607b0710d12aaabd17fd053d83.png)
求(i)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34ecc467cf90f9f26cf6902af77427ca.png)
(ii)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0d0e78101fef36a75b70ac7e7cf5b.png)
您最近一年使用:0次
2023-01-03更新
|
874次组卷
|
3卷引用:北京市海淀实验中学2023届高三上学期期末数学试题
北京市海淀实验中学2023届高三上学期期末数学试题第八章立体几何初步章节验收测评卷-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)重难点突破02 利用传统方法求线线角、线面角、二面角与距离(四大题型)
名校
4 . 如图,
和
都垂直于平面
,
是
上一点,且
,
为等腰直角三角形,且
是斜边
的中点,
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/d8adbf38-85ba-4d6a-b98b-7680ff33e7f3.png?resizew=167)
(1)证明:
平面
;
(2)求二面角
的平面角的正切值;
(3)若点P是平面ADE内一点,且
,设点P到平面ABE的距离为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b1c22e1a7bb01c795b34b0b323ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/d8adbf38-85ba-4d6a-b98b-7680ff33e7f3.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/befd9ccddb75aeb71cd1a008669f34da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395de6d5d6b0073af625ae32a4abf9a1.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1befad21888ca33d1d6be4acbe7bbd95.png)
(3)若点P是平面ADE内一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026ec361327730d3c614a6f25b9b994f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c002e76ec64a9a1922c93a8a51d48426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
您最近一年使用:0次
2022-07-10更新
|
922次组卷
|
9卷引用:第04讲 空间直线、平面的垂直 (练)
(已下线)第04讲 空间直线、平面的垂直 (练)湖北省武汉市第十九中学2022-2023学年高二上学期10月月考数学试题湖北省武汉市第三中学2022-2023学年高二上学期10月月考数学试题河南省南阳市桐柏县第一高级中学2022-2023学年高一下学期期末数学试题(已下线)高一下学期期末真题精选(压轴60题20个考点专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)辽宁省沈阳市第十一中学2023-2024学年高二上学期10月月考数学试题浙江省台州市路桥中学2023-2024学年高二上学期10月月考数学试题(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)湖北省部分市州2021-2022学年高一下学期7月期末联考数学试题
5 . 正多面体也称柏拉图立体,被喻为最有规律的立体结构,其所有面都只由一种正多边形构成的多面体(各面都是全等的正多边形,且每一个顶点所接的面数都一样,各相邻面所成二面角都相等).数学家已经证明世界上只存在五种柏拉图立体,即正四面体、正六面体、正八面体、正十二面体、正二十面体.已知一个正四面体
和一个正八面体
的棱长都是a(如图),把它们拼接起来,使它们一个表面重合,得到一个新多面体.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/eaf15142-da03-42ca-8aba-80d34458cc28.png?resizew=320)
(1)求新多面体的体积;
(2)求二面角
的余弦值;
(3)求新多面体为几面体?并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb6c9306a25f041d7801274838b43dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87bc797aad25e4ccdc9d722a87b642c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/eaf15142-da03-42ca-8aba-80d34458cc28.png?resizew=320)
(1)求新多面体的体积;
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b820c84570da9c38d0a81c22788b76.png)
(3)求新多面体为几面体?并证明.
您最近一年使用:0次
2021-05-11更新
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977次组卷
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7卷引用:辽宁省葫芦岛市2021届高三一模数学试题
辽宁省葫芦岛市2021届高三一模数学试题(已下线)专题06 空间图形的表面积和体积-2020-2021学年高一数学下学期期末专项复习(苏教版2019必修第二册)辽宁省名校2021届高三第一次联考数学试题辽宁省沈阳市第一二〇中学2021-2022学年高二上学期期初质量监测数学试题(已下线)11.3 多面体与旋转体(四大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)第六章 突破立体几何创新问题 专题二 交汇世界文化 微点2 与世界文化遗产有关的的立体几何问题综合训练【基础版】江苏省苏州市昆山市周市高级中学2021-2022学年高三上学期暑期网课自主学习测试数学试题