名校
1 . 如图,在四棱锥
中,底面
是梯形,
,
平面
,点
是棱
上的一点.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2992510187610112/2996945677328384/STEM/0c24e0d0-485d-46bf-9e7e-6200a21eddc0.png?resizew=229)
(1)若
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
平面
;
(2)若
是
的中点,求二面角
的余弦值.
![](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/014d97ca1baea8247a0b458224e32052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b31276ae0fe54a379e92cddce38edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2992510187610112/2996945677328384/STEM/0c24e0d0-485d-46bf-9e7e-6200a21eddc0.png?resizew=229)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482fa6ee95b8e38d578d8e24fcf44d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64785e4401e1d79632e360fd3626ed62.png)
您最近一年使用:0次
2022-06-08更新
|
1588次组卷
|
4卷引用:安徽省六安市舒城中学2022-2023学年高二上学期第二次月考数学试题
名校
2 . 如图,在三棱柱
中,所有棱长均为
.
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942537901555712/2943933300137984/STEM/c8f9e0e7416d48fdaa590a0f24436a6f.png?resizew=174)
(1)证明:平面
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d6fca51a92ac9661030a795657fc58.png)
![](https://img.xkw.com/dksih/QBM/2022/3/23/2942537901555712/2943933300137984/STEM/c8f9e0e7416d48fdaa590a0f24436a6f.png?resizew=174)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ffdb9543ecf8a3bcdd2e09c2d4e9a8.png)
您最近一年使用:0次
2022-03-25更新
|
1599次组卷
|
5卷引用:安徽省合肥市第十中学2021-2022学年高二下学期期末模拟数学试题1
解题方法
3 . 如图,在四棱锥
中,底面ABCD为直角梯形,
,
平面ABCD,
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897166342520832/2914130945433600/STEM/d452ff19-ff05-4bb7-a10a-40c5d8ef50d0.png?resizew=181)
(1)求点B到平面PCD的距离;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d3947804a878a87052c266be475423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671b73222413dd075d70bfbb2b1dfb91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897166342520832/2914130945433600/STEM/d452ff19-ff05-4bb7-a10a-40c5d8ef50d0.png?resizew=181)
(1)求点B到平面PCD的距离;
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
您最近一年使用:0次
2022-02-11更新
|
300次组卷
|
3卷引用:安徽省宿州市十三所重点中学2021-2022学年高二上学期期末质量检测数学试题
名校
解题方法
4 . 如图,已知圆
的直径
长为4,点
是圆弧上一点,
,点
是劣弧
上的动点,
点是另一半圆弧的中点,沿直径
,将圆面折成直二面角,连接
.
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892240271745024/2910421359943680/STEM/ee046130-97aa-499e-935e-3142c07746e4.png?resizew=349)
(1)若
面
时,求
的长;
(2)当三棱锥
体积最大时,求二面角
正切值.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfb836792b1eebfbd08a6f46fae580e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16f6efa10501511dd7c63c5051376c7.png)
![](https://img.xkw.com/dksih/QBM/2022/1/11/2892240271745024/2910421359943680/STEM/ee046130-97aa-499e-935e-3142c07746e4.png?resizew=349)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8099c774a6ae6dd98712b0b90b60cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2a4541d85e8710408c45c99950b6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0297943fae12e34fab38c541002b15.png)
您最近一年使用:0次
2022-02-06更新
|
1010次组卷
|
6卷引用:安徽省亳州市第一中学2021-2022学年高二上学期元月月考数学试题
安徽省亳州市第一中学2021-2022学年高二上学期元月月考数学试题安徽省合肥市第一中学2021-2022学年高二下学期3月测试数学试题安徽省淮北市2022届高三上学期一模理科数学试题(已下线)山东省日照市2023届高三一模考试数学试题变式题17-22河北省唐山市开滦第二中学2023届高三考前保温数学试题(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点8 平面图形的翻折、旋转综合训练
名校
5 . 如图,在等腰直角三角形
中,
分别是
上的点,且
分别为
的中点,现将
沿
折起,得到四棱锥
,连接![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23853b5555468f9d803713d1d9353750.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/3e6740be-3953-4f28-91ea-930c1735e3f6.png?resizew=400)
(1)证明:
平面
;
(2)在翻折的过程中,当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084ce748ea72556d4d575d84d0ea594f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6b04dcd5a34b8125696faf552ab63f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79c1b3d8a1ea4d9370996706199e5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0fa96c746ceab61c043cbb95b7d2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23853b5555468f9d803713d1d9353750.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/3e6740be-3953-4f28-91ea-930c1735e3f6.png?resizew=400)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在翻折的过程中,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2022-06-18更新
|
1513次组卷
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11卷引用:安徽省淮南一中2020-2021学年高二下学期开学考理科数学试题
安徽省淮南一中2020-2021学年高二下学期开学考理科数学试题安徽省江淮名校2020-2021学年高二下学期开学联考数学(理)试题陕西省西安市长安区第一中学2020-2021学年高二上学期期末数学(理)试题湖北省宜昌市示范高中教学协作体2021-2022学年高二上学期期中数学试题贵州省遵义市第五中学2021-2022学年高二上学期期中考试数学(理)试题吉林省松原市宁江区吉林油田高级中学2021-2022学年高二上学期期初数学考试试题(已下线)1.2.4 二面角(已下线)专题9.10—立体几何—二面角2—2022届高三数学一轮复习精讲精练福建省福州第一中学2021-2022学年高一下学期期末考试数学试题(已下线)专题24 立体几何解答题最全归纳总结-1(已下线)第07讲 向量法求距离、探索性及折叠问题 (练)
6 . 在正方体
中,
分别为
的中点,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/28/2989280709353472/2990801510023168/STEM/4d9e6ed9-277a-4a21-893b-f0edecb84866.png?resizew=196)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557a1bc648125cc09cb63412bc13ea1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ce0e22c4edc6ef768e0c12f59e483.png)
![](https://img.xkw.com/dksih/QBM/2022/5/28/2989280709353472/2990801510023168/STEM/4d9e6ed9-277a-4a21-893b-f0edecb84866.png?resizew=196)
A.![]() |
B.二面角![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.点![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-05-30更新
|
2855次组卷
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9卷引用:安徽省芜湖市第一中学2022-2023学年高二上学期第一次阶段性诊断测试数学试题
安徽省芜湖市第一中学2022-2023学年高二上学期第一次阶段性诊断测试数学试题江苏省扬州中学2020-2021学年高二下学期期中数学试题(已下线)卷02 空间向量与立体几何-单元检测(中)-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)广东省广州市协和中学2021-2022学年高二上学期期中数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)江苏省盐城市响水中学2021-2022学年高一下学期第二次学情分析考试数学试题(已下线)2022年全国新高考Ⅰ卷数学试题变式题20-22题(已下线)第04讲 空间直线、平面的垂直 (练)(已下线)2022年全国新高考Ⅰ卷数学试题变式题9-12题
7 . 如图,在四棱锥
中,底面
满足
平面
,且
.
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872422041985024/2948680346017792/STEM/5e8825be67364788b6fbf7f7629eb568.png?resizew=184)
(1)证明:
平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d101cd311efd7e9cf066eb7a4136313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adb8e53cd26c16216a001eeb84dc7e7.png)
![](https://img.xkw.com/dksih/QBM/2021/12/14/2872422041985024/2948680346017792/STEM/5e8825be67364788b6fbf7f7629eb568.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
您最近一年使用:0次
2022-04-01更新
|
413次组卷
|
2卷引用:安徽省六安中学2021-2022学年高二上学期期中理科数学试题
名校
解题方法
8 . 如图,在直三棱柱ABC﹣A1B1C1中,AA1=AC=4,AB=3,BC=5,点D是线段BC的中点.
(2)求二面角D﹣CA1﹣A的余弦值;
(2)求二面角D﹣CA1﹣A的余弦值;
您最近一年使用:0次
2021-11-22更新
|
616次组卷
|
7卷引用:安徽省六安市舒城晓天中学2022-2023学年高二上学期期中数学试题
名校
9 . 如图,在四棱锥E-ABCD中,平面CDE⊥平面ABCD,∠ABC=∠DAB=90°,EC=AD=2,AB=BC=1,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/e4b51493-aad3-4d75-94d4-e21b4e2ceede.png?resizew=188)
(1)证明:AB⊥平面ADE;
(2)求二面角C-AE-D的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520e410203db295a838426752b991eef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/e4b51493-aad3-4d75-94d4-e21b4e2ceede.png?resizew=188)
(1)证明:AB⊥平面ADE;
(2)求二面角C-AE-D的大小.
您最近一年使用:0次
2022-03-27更新
|
686次组卷
|
4卷引用:安徽省合肥市第六中学2020-2021学年高二上学期期中数学(理)试题
名校
解题方法
10 . 如图,正方体
的棱长为2,E,F分别为
,
的中点,则以下说法错误 的是_______ (写序号)
![](https://img.xkw.com/dksih/QBM/2021/10/11/2827124316356608/2827831393984512/STEM/75cc7f97a338430081fff48b4485d2cf.png?resizew=206)
①N为
上一点,则平面
与平面
所成二面角的大小与点N位置无关;②
存在上一点P,使得
平面
;③ 三棱锥
和
体积相等;④
上存在一点M,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/2021/10/11/2827124316356608/2827831393984512/STEM/75cc7f97a338430081fff48b4485d2cf.png?resizew=206)
①N为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a681d311a864d38cf306a0c137cbcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5ce42fe8ea626c297e3b2a2ab95149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d862fc2fe541999e0c175d32e90a81ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209e3b87346e057276f0692a7361e446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e576dc99511316d17ad2bbcbdaedc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8076abdfd96e1b717a18c155557a02f.png)
您最近一年使用:0次