名校
解题方法
1 . 现有如图所示的八面体,八面体的正视图和侧视图如图所示.
(1)证明:
面BEC;
(2)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/27/5cad00b9-16a6-4b0d-b442-840de4667213.png?resizew=457)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2b5cfae407016cad45bbdefea05833.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c539709f3b8449ef9cd00a86e194c099.png)
您最近一年使用:0次
名校
解题方法
2 . 如图1,在
中,
是直角,
,
是斜边
的中点,
分别是
的中点.沿中线
将
折起,连接
,点
是线段
上的动点,如图2所示.
平面
;
(2)从条件①、条件②这两个条件中选择一个条件作为已知,当二面角
的余弦值为
时.求
的值.
条件①:
;条件②:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a392fbab2cec9be35961f28599960ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589c3cc1f331dbb2248b0829039df7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b13964019381c4cd9de05f95c4261b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)从条件①、条件②这两个条件中选择一个条件作为已知,当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d270aaceaef31f79bfc175e9cc7528d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856fd4db1f61969fb500f5a2c220fb73.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09a88dc7dc9cd668a57138e1ec71ea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
您最近一年使用:0次
2023-01-03更新
|
857次组卷
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6卷引用:四川省成都市石室中学2023届高三下学期高考专家联测卷(四)数学(理)试题
四川省成都市石室中学2023届高三下学期高考专家联测卷(四)数学(理)试题四川省绵阳实验高级中学2023届高三第6次模拟测试理科数学试题(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题16-21四川省绵阳中学2023届高三理科数学模拟(二)北京市石景山区2022-2023学年高二上学期数学期末试题(已下线)6.3.3空间角的计算(1)
名校
解题方法
3 . 如图,已知正方体
的棱长为2,M,N分别为
,
的中点.有下列结论:
在平面
上的正投影图为等腰三角形;
②直线
平面
;
③在棱BC上存在一点E,使得平面
平面
;
④若F为棱AB的中点,且三棱锥
的各顶点均在同一求面上,则该球的体积为
.
其中正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5697ef048e910e7b85ed6bac01056362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b808a8facf9af30cd8a083010a7b850d.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
③在棱BC上存在一点E,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcadc521b53fabecc10ed30fe8d96c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee5a94f9063a71581f409e47ebaf602.png)
④若F为棱AB的中点,且三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b5d7a90614288e46bebdb611e9bd23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefdcd39676298f214654051fc51ba92.png)
其中正确结论的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
2022-07-12更新
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3160次组卷
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12卷引用:四川省成都市2023届高三上学期摸底考试文科数学试题
四川省成都市2023届高三上学期摸底考试文科数学试题四川省成都市2023届高三摸底测试理科数学试题安徽省宣城中学2023届高三原创模拟金卷(一)数学试题(已下线)第04讲 空间直线、平面的垂直 (讲)-1(已下线)考向25空间几何体的结构、三视图和直观图(重点)(已下线)考向26空间几何体的表面积与体积(重点)-2第一章 空间向量与立体几何单元测试(巅峰版)山西省运城市景胜中学2022-2023学年高二上学期9月月考数学(A)试题河南省南阳市第八中学校2022-2023学年高二上学期第一次线上考试(月考)数学试题广东省珠海市斗门区第一中学2022-2023学年高二上学期期中数学试题天津市新四区示范校2022-2023学年高一下学期期末联考数学试题河南省周口市周口恒大中学2023-2024学年高二下学期5月月考数学试题
名校
解题方法
4 . 正方体
的棱长为2,正方形
的心分别是
,
,且
分别是棱
上的动点(含端点),其中
关于点
对称,
关于点
对称,
,则下列结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d588432f768c53e5bace86c520cd8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc78609d71a170e9dc5c481c44fede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de64cbea23ec8a57a4705d9f16297d80.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/24/d1f47a3d-2609-449b-913f-72d4bcc7ca92.png?resizew=247)
A.若四点![]() ![]() ![]() ![]() |
B.若四点![]() ![]() ![]() ![]() |
C.四面体![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2022-05-22更新
|
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4卷引用:四川省成都市名校2022-2023学年高三下期4月定时训练文科数学试题
四川省成都市名校2022-2023学年高三下期4月定时训练文科数学试题安徽省江淮名校2022届高三下学期5月联考理科数学试题湖北省黄石市2023届高三下学期高考适应性训练数学试题(已下线)突破1.4 空间向量的应用(课时训练)
名校
5 . 已知△ABC是边长为6的等边三角形,点M,N分别是边AB,AC的三等分点,且
,
,沿MN将△AMN折起到
的位置,使
.
![](https://img.xkw.com/dksih/QBM/2022/3/21/2941122016854016/2941973344141312/STEM/2e8e1f2861954c9687b97882d744e8d7.png?resizew=424)
(1)求证:
平面MBCN;
(2)在线段BC上是否存在点D,使平面
与平面
所成锐二面角的余弦值为
?若存在,设
,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba486b7a12ec874644dc5fea93a56916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a45b6f1348711bc6eabd87982c3756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e7040c2fd8a163d71e35805775feb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d938067915b0d59f491b4c8ee7a982.png)
![](https://img.xkw.com/dksih/QBM/2022/3/21/2941122016854016/2941973344141312/STEM/2e8e1f2861954c9687b97882d744e8d7.png?resizew=424)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eedf1e774ce129d9a09f02ca1920052.png)
(2)在线段BC上是否存在点D,使平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4459d0d7b4c2e9e8106fe5b4520277e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c932cfbb9fb63159a176a8f45489a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e108d5c61e85e0741ec2c484fc5768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2f0857ee6d2e3e5341bcc916f2e067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-03-22更新
|
3708次组卷
|
7卷引用:四川省成都市第七中学2022-2023学年高三上期一诊模拟考试数学(理)试题
名校
解题方法
6 . 如图甲,在直角三角形
中,已知
,
,
,D,E分别是
的中点.将
沿
折起,使点A到达点
的位置,且
,连接
,得到如图乙所示的四棱锥![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2792f6f1fde407c93201c0f3fad39d52.png)
,M为线段
上一点.
![](https://img.xkw.com/dksih/QBM/2021/12/27/2881711704768512/2883062489751552/STEM/fec3dcb7-0cff-40c0-b9e1-a756f6dfb4bb.png?resizew=286)
(1)证明:平面
平面
;
(2)过B,C,M三点的平面与线段A'E相交于点N,从下列三个条件中选择一个作为已知条件,求直线DN与平面A'BC所成角的正弦值.
①
;②直线
与
所成角的大小为
;③三棱锥
的体积是三棱锥
体积的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77a22740bd1ad5f5979e4579cb177d0.png)
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4772895af07cae75fc85a48507952c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7b7e2f8b77c8a8518198511b458233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2792f6f1fde407c93201c0f3fad39d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1333acc72211e3ddb9a0f8c726ce8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a21897349d3d7c94419692106887153.png)
![](https://img.xkw.com/dksih/QBM/2021/12/27/2881711704768512/2883062489751552/STEM/fec3dcb7-0cff-40c0-b9e1-a756f6dfb4bb.png?resizew=286)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789069cf57bd1059f5e0f9ac61d933b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1333acc72211e3ddb9a0f8c726ce8a5.png)
(2)过B,C,M三点的平面与线段A'E相交于点N,从下列三个条件中选择一个作为已知条件,求直线DN与平面A'BC所成角的正弦值.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f8da1f66714eba7f2867a19d02479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee48b4d6b9ee347b2ba6305f2fdc2bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04aab7c8fe102e94d113cad242921a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77a22740bd1ad5f5979e4579cb177d0.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2021-12-29更新
|
938次组卷
|
3卷引用:四川省成都市2021-2022学年高三第一次诊断性检测理科数学试题
7 . 如图,
,
分别是圆台上下底面的圆心,
是下底面圆的直径,
,点
是下底面内以
为直径的圆上的一个动点(点
不在
上).
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720310018605056/2720901185110016/STEM/4ef06bd6-47d9-485d-919c-6f787b33f55c.png?resizew=286)
(Ⅰ)求证:平面
平面
;
(Ⅱ)若
,
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d40a9e1d9a88d1045731e8dbc16b78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6973bc602348065901b58bb1b4e6bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6973bc602348065901b58bb1b4e6bb3.png)
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720310018605056/2720901185110016/STEM/4ef06bd6-47d9-485d-919c-6f787b33f55c.png?resizew=286)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b53e60ab704a67ecabda3d3166a59a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4ea944027f8d8edcdf305c41f36c1f.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849ca2978032a5af95c7f9ce419b594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16bab906d4fc26acb1a7f681a3bb2981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaed3f5ee2d7e2831a695d0953fb9567.png)
您最近一年使用:0次
2021-05-14更新
|
923次组卷
|
10卷引用:四川省成都玉林中学2023届高三下学期二诊考试理科数学模拟试题
四川省成都玉林中学2023届高三下学期二诊考试理科数学模拟试题山西省太原市2021届高三三模数学(理)试题江苏省南京市金陵中学2021-2022学年高三上学期学情检测考前热身数学试题(已下线)一轮复习大题专练54—立体几何(二面角3)-2022届高三数学一轮复习黑龙江省佳木斯市第二中学2021-2022学年高三第三次月考数学(理)试题上海市高桥中学2023届高三上学期9月月考数学试题四川省泸州市泸县第四中学2022-2023学年高三下学期第二次诊断性模拟考试数学(理)试题四川省泸县第四中学2023届高三第二次诊断性模拟考试数学(理科)试题四川省绵阳南山中学2023届高三下学期高考热身考试理科数学试题江苏省宿迁市泗阳县实验高级中学2021-2022学年高二下学期第一次月考数学试题