名校
1 . 如图所示,正方形
与梯形
所在的平面互相垂直,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/662cf6ff-1732-4238-953f-0b4a263eeba5.png?resizew=192)
(1)求证:
平面
;
(2)求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c9773e77146de880f1204dd9ef4593.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/662cf6ff-1732-4238-953f-0b4a263eeba5.png?resizew=192)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
您最近一年使用:0次
2022-04-10更新
|
523次组卷
|
2卷引用:江苏省盐城市响水县第二中学2021-2022学年高二(11-18班)下学期期中数学试题
名校
解题方法
2 . 如图,在直四棱柱
中,底面四边形
为梯形,点
为
上一点,且
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/6/5/2736394871193600/2737819917500416/STEM/81210a37863449af8959795daea8687a.png?resizew=144)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/2b86cde4e24036082b9c92253a6f579e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5d3aaafa4e988aee932be29cf5ac0e.png)
![](https://img.xkw.com/dksih/QBM/2021/6/5/2736394871193600/2737819917500416/STEM/81210a37863449af8959795daea8687a.png?resizew=144)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c8f2410d6a17adcf6817b08d20f3ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ded2e3fdcab984f3699972fc3ff75d5.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4294ffdba16ae69fd03b13959d682aba.png)
您最近一年使用:0次
2021-06-07更新
|
822次组卷
|
6卷引用:山西大学附属中学2022届高三上学期11月期中数学(文)试题
山西大学附属中学2022届高三上学期11月期中数学(文)试题山西省吕梁学院附属高级中学2022届高三上学期期中数学(文)试题安徽省蚌埠市第二中学2021届高三下学期高考最后一模文科数学试题四川省遂宁市2021届高三三模数学(文)试题(已下线)考点32 直线、平面平行的判定及其性质-备战2022年高考数学(文)一轮复习考点帮河南省名校联盟2021-2022学年上学期高三第一次诊断考试文科数学试题
名校
3 . 如图,三棱柱
中侧棱与底面垂直,且AB=AC=2,AA1=4,AB⊥AC,M,N,P,D分别为CC1,BC,AB,
的中点.
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
(2)求平面PMN与平面ACC1A1所成锐二面角的余弦值.
您最近一年使用:0次
名校
4 . 如图,在矩形ABCD和矩形ABEF中,
,
,矩形ABEF可沿AB任意翻折.
![](https://img.xkw.com/dksih/QBM/2020/1/30/2388354048933888/2389111775379456/STEM/6a2facb046bc42008ce9a5231af6ca75.png?resizew=123)
(1)求证:当点F,A,D不共线时,线段MN总平行于平面ADF.
(2)“不管怎样翻折矩形ABEF,线段MN总与线段FD平行”这个结论正确吗?如果正确,请证明;如果不正确,请说明能否改变个别已知条件使上述结论成立,并给出理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22437a2a3402609bfd4054a9f2b6c685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ff398bdaa4eb5a274f86c0d8b77ef2.png)
![](https://img.xkw.com/dksih/QBM/2020/1/30/2388354048933888/2389111775379456/STEM/6a2facb046bc42008ce9a5231af6ca75.png?resizew=123)
(1)求证:当点F,A,D不共线时,线段MN总平行于平面ADF.
(2)“不管怎样翻折矩形ABEF,线段MN总与线段FD平行”这个结论正确吗?如果正确,请证明;如果不正确,请说明能否改变个别已知条件使上述结论成立,并给出理由.
您最近一年使用:0次
2020-01-31更新
|
1079次组卷
|
9卷引用:云南省昆明市第八中学2020-2021学年高一下学期期中考试数学试题
云南省昆明市第八中学2020-2021学年高一下学期期中考试数学试题人教B版(2019) 必修第四册 逆袭之路 第十一章 立体几何初步 11.3.3 平面与平面平行人教A版(2019) 必修第二册 逆袭之路 第八章 8.5 空间直线、平面的平行 8.5.3 平面与平面平行人教B版(2019) 必修第四册 过关斩将 第十一章 立体几何初步 11.3.3 平面与平面平行(已下线)【新教材精创】11.3.2直线与平面平行(第2课时)练习(1)(已下线)8.5空间直线、平面的平行C卷苏教版(2019) 必修第二册 过关斩将 第13章 13.2 综合拔高练(已下线)专题8.10 空间直线、平面的平行(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)新疆维吾尔自治区乌鲁木齐市米东区乌鲁木齐市第101中学2023届高三上学期1月月考数学试题
名校
5 . 如图,在四面体
中,
平面
是
的中点,
是
的中点,点
满足
.
(1)证明:
平面
;
(2)若
与平面
所成的角大小为
,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999c8f0e34d080fbbc53f97e5317bbb6.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/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91f0750166d53342ab1db4f85dee0f8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/acb00f66-5b21-4743-843c-eed0ccffedfd.png?resizew=131)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2023-11-11更新
|
212次组卷
|
2卷引用:浙江省浙东北联盟(ZDB)2023-2024学年高二上学期期中数学试题
名校
6 . 已知四棱锥
中,底面
为平行四边形,点
、
、
分别在
、
、
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/b48f20ce-0a89-4697-a1a0-af73a52c3dee.png?resizew=180)
(1)若
,求证:平面
平面
;
(2)若
满足
,则
点满足什么条件时,
面
.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/b48f20ce-0a89-4697-a1a0-af73a52c3dee.png?resizew=180)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480eb43bbb9a6e3ef0c7cc491e860b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28a07491270be75a3697538bec706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b784a3ef1d564942190c27ef4c98578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7ffa7d57cb72ca3468f448e70b52af.png)
您最近一年使用:0次
2019-10-06更新
|
1465次组卷
|
4卷引用:广东省广州市第十六中学2020-2021学年高一下学期期中数学试题
名校
解题方法
7 . 如图,四边形
与
均为菱形,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/5865decd-e504-4687-809e-197f7fba2f3f.png?resizew=200)
(1)求证:平面
平面
;
(2)求证:
平面
;
(3)求二面角
的余弦值.
![](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/6da20f949db06cbc10f052a7f8466019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f944d655ba3e2325d5a95a01e6ff85.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/5865decd-e504-4687-809e-197f7fba2f3f.png?resizew=200)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ce82a4c37365f2d4dea2c4ad2e3288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111da2c687a67fd089c365090908eb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2194add18a7df1a23cf1554dc2da1b40.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed7a8116d2f02b52c33fb7a49fc0d1ae.png)
您最近一年使用:0次
2020-12-02更新
|
1095次组卷
|
3卷引用:黑龙江省哈尔滨师范大学附属中学2020-2021学年高三上学期期中考试数学(理)试题
名校
8 . 如图,C,D分别是以AB为直径的半圆O上的点,满足
,△PAB为等边三角形,且与半圆O所成二面角的大小为90°,E为PA的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/3a73e84a-27cb-4df4-a354-5424ece967b6.png?resizew=138)
(1)求证:DE//平面PBC;
(2)求二面角A-BE-D的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e925392d0bf25a1a5c698ec1d8adea4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/3a73e84a-27cb-4df4-a354-5424ece967b6.png?resizew=138)
(1)求证:DE//平面PBC;
(2)求二面角A-BE-D的余弦值.
您最近一年使用:0次
2022-01-29更新
|
440次组卷
|
3卷引用:海南省洋浦中学2022-2023学年高二下学期期中数学试题
名校
解题方法
9 . 如图,在三棱柱
中,
平面
,
,
,
,
是棱
的中点,
在棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/0d2f5ae9-f81a-486c-b138-5b097f5f4860.png?resizew=155)
(1)在棱
上是否存在点
,满足
平面
,若存在,求出
的值;
(2)在(1)的条件下,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a9169fcd233a32ceeaa307dc6e4cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb0c5356f71d651ef82e5bcce9019b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/0d2f5ae9-f81a-486c-b138-5b097f5f4860.png?resizew=155)
(1)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)在(1)的条件下,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2021-05-28更新
|
709次组卷
|
2卷引用:四川省成都市树德中学2021-2022学年高三上学期11月阶段性测试(期中)数学(理)试题
名校
解题方法
10 . 如图所示的平行六面体
中,已知
,
,
,
为
上一点,且
,点
棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2b5a914d-fbf1-499c-8feb-3424a4eec78f.png?resizew=215)
(1)用
,
,
表示
;
(2)若
,求
;
(3)若
,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1132330203ed3270a52e0fbd0f34e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13601fc499850fce16debbab6c627ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d76ebfa48fbd7a62488731294de8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28408efa93ec310ccdf156c02fc6c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14184f726fecb76ac6ab3f0b6dfd6f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/2b5a914d-fbf1-499c-8feb-3424a4eec78f.png?resizew=215)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7559d65befe0b85c8929f57c9436cd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4648d56ec5ba86c288bc22737250ba0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc14c781097654ee29b6b5435c31480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a114d968325e799e60de7ae82d1936.png)
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