1 . 如图,在正方体
中,
,
为上底面
的中心.
;
(2)求点
到平面
的距离;
(3)判断棱
上是否存在一点
,使得
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d6b98ecb4793c9f063f1f6b61caa19.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(3)判断棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b18c0b2b38a140896f65eb3d3f942c1.png)
您最近一年使用:0次
解题方法
2 . 如图,在正方体
中,E为
的中点,F为正方体棱的中点,则满足条件直线
平面
的点F的个数是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
2022-07-09更新
|
1569次组卷
|
9卷引用:北京市通州区2021-2022学年高一下学期期末质量检测数学试题
北京市通州区2021-2022学年高一下学期期末质量检测数学试题(已下线)第03讲 空间直线、平面的平行 (精讲)-2(已下线)第八章 立体几何初步 (单元测)(已下线)8.5.2 直线与平面平行(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)专题强化三 直线、平面的平行和垂直问题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)模块二 专题4 立体几何中的平行与垂直的位置关系 能力卷B(已下线)模块二 专题7 立体几何中的平行与垂直的位置关系 能力卷B(已下线)核心考点07空间直线、平面的平行-【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)(已下线)专题06 空间中点线面的位置关系6种常考题型归类(1)-期期末真题分类汇编(北京专用)
解题方法
3 . 如图,在四棱柱
中,侧棱
底面
,四边形
为菱形,
,E,F分别为
的中点.
平面
,并求点C到平面
的距离;
(2)证明:
四点共面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.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/1e77db8e97cf0910fec52f526d0e4b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e86e3991200297ad172455e5ea93f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc78a86b12ba0b4553135a3a635fc418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc78a86b12ba0b4553135a3a635fc418.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da066c1fd31a8271a7c2c73d089a27d.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在四棱锥
中,底面
为梯形,
,
,
,
,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/18/2896988979838976/2901599572762624/STEM/3a4a68af-8f5e-4b31-9f9a-326cd24a07e1.png?resizew=214)
(1)判断直线
与
的位置关系,并说明理由;
(2)求二面角
的余弦值;
(3)求点
到平面
的距离.
![](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/4a1c9d4808c72fb8e4c885e236d62967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49437f474e5805688dff21ded2d1fd7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbca4e9beec36d7e8286e6e5dca7ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0607224c3bf82e279c3ba0dbe46fa036.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/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2896988979838976/2901599572762624/STEM/3a4a68af-8f5e-4b31-9f9a-326cd24a07e1.png?resizew=214)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-01-24更新
|
547次组卷
|
2卷引用:北京市门头沟区2022届高三上学期期末调研数学试题
解题方法
5 . 点
是正方体
的底面
内(包括边界)的动点.给出下列三个结论:
①满足
的点
有且只有
个;
②满足
的点
有且只有
个;
③满足
平面
的点
的轨迹是线段.
则上述结论正确的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
①满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e60da1e6b2612196b2c65d4e4042b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
②满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c01029f177a515698802e6c6cf06d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
③满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899d637fe4107582fbbbdf6fc6304513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
则上述结论正确的个数是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
6 . 如图1,在△
中,
,
为
中点,
于
,延长
交
于
.将△
沿
折起,得到三棱锥
,如图2所示.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572677790146560/1572677796093952/STEM/9c729c9b81f34a479ad7fa4d98830b17.png)
(Ⅰ)若
是
的中点,求证:
∥平面
;
(Ⅱ)若平面
平面
,试判断直线
与直线
能否垂直?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde6182c16084365446aac3c4475d808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6863529cecdf22e3488ab99d75f89d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](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/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b97b7e45a628d3e5b4d42ce924dce28.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572677790146560/1572677796093952/STEM/9c729c9b81f34a479ad7fa4d98830b17.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
(Ⅱ)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c53647b9072e89d95914d7b532ff18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2016-12-04更新
|
397次组卷
|
2卷引用:2015-2016学年北京市西城区高二上学期期末考试文科数学试卷
7 . 如图,在四棱锥
中,底面ABCD是菱形,PA=PB,且侧面PAB⊥平面ABCD,点E是AB的中点.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572676961976320/1572676967432192/STEM/de2466a7ffc5483199818bb34e6d3a19.png)
(Ⅰ)求证:CD∥平面PAB;
(Ⅱ)求证:PE⊥AD.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572676961976320/1572676967432192/STEM/8b0e9416f13946b9ae3be3e05256295e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572676961976320/1572676967432192/STEM/de2466a7ffc5483199818bb34e6d3a19.png)
(Ⅰ)求证:CD∥平面PAB;
(Ⅱ)求证:PE⊥AD.
您最近一年使用:0次
8 . 已知:四棱锥P-ABCD,
,底面ABCD是直角梯形,
,且AB∥CD,
, 点F在线段PC上运动.
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/1cdbddd6c0fa462e877dc18f2744fef0.png)
(Ⅰ) 当F为PC的中点时,求证:BF∥平面PAD;
(Ⅱ)设
,求当
为何值时有
.
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/87d0ee1ede5148d7ace98d3810181523.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/d6a669641bc9447791778d5786938906.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/c318c480dba34617933c85c6905d6477.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/1cdbddd6c0fa462e877dc18f2744fef0.png)
(Ⅰ) 当F为PC的中点时,求证:BF∥平面PAD;
(Ⅱ)设
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/f9f20c2c8f394cc19c00d87254db00cd.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/1c180b6f322f4e5894e1e6c6316279bf.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572631842357248/1572631848484864/STEM/2a9d1d9c0da84f5ba8db2fde39f5cf91.png)
您最近一年使用:0次
9 . 如图是正方体的平面展开图,在这个正方体中,正确的命题是
![](https://img.xkw.com/dksih/QBM/2019/2/26/2149120719814656/2153938962792449/STEM/be72ed339bd74d3db8fabdae031867e8.png?resizew=155)
![](https://img.xkw.com/dksih/QBM/2019/2/26/2149120719814656/2153938962792449/STEM/be72ed339bd74d3db8fabdae031867e8.png?resizew=155)
A.BD与CF成60°角 | B.BD与EF成60°角 | C.AB与CD成60°角 | D.AB与EF成60°角 |
您最近一年使用:0次
2016-12-04更新
|
542次组卷
|
4卷引用:【全国百强校】北京101中学2018-2019学年高二上学期期末考试数学试题