名校
解题方法
1 . 如图所示,底面为正方形的四棱锥
中,
,
,
,AC与BD相交于点O,E为PD中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/35d77407-322f-4a97-9b6f-097fc9945441.png?resizew=156)
(1)求证:
平面ABCD;
(2)点F是AD的中点,作出平面OEF截四棱锥所成截面并求截面的面积.(说明作图过程并证明、求解)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4ad370fe836accc1b2de6807d8ae62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/35d77407-322f-4a97-9b6f-097fc9945441.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
(2)点F是AD的中点,作出平面OEF截四棱锥所成截面并求截面的面积.(说明作图过程并证明、求解)
您最近一年使用:0次
名校
解题方法
2 . 如图所示,已知四边形ABCD是正方形,四边形ACEF是矩形,M是线段EF的中点.
平面BDE;
(2)若平面
平面
,平面
平面
,试分析l与m的位置关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3e2deda1ce6ec95b5e89220e826b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48abba67b697688749cf92b8c7205161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24462999a96dfae3b4123ef4c59a48ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2685e63e66cd2c9a048590bc0f16d.png)
您最近一年使用:0次
2022-05-03更新
|
975次组卷
|
6卷引用:福建省漳州第三中学2021-2022学年高一下学期期中考试数学试题
福建省漳州第三中学2021-2022学年高一下学期期中考试数学试题(已下线)第11练 空间直线、平面的平行-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)(已下线)第03讲 直线、平面平行垂直的判定与性质(讲)江苏省扬州市宝应区曹甸高级中学2022-2023学年高三上学期第一次月考数学试题浙江省金华市曙光学校2023-2024学年高一下学期4月月考数学试题(已下线)必考考点5 立体几何中的位置关系 专题讲解 (期末考试必考的10大核心考点)
名校
解题方法
3 . 如图,在三棱柱
中,侧面
是菱形,G是边
的中点.平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2020/10/20/2575283505111040/2578114044436480/STEM/bda0f61dc51048a48acc9ddc2cca33e9.png?resizew=215)
(1)求证:
;
(2)在线段
上是否存在点M,使得
平面
,若存在,请说明M点的具体位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2e00a3b5d4f1e10a52058f148060d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb64353c99068a7a1a8508a22f5b25b4.png)
![](https://img.xkw.com/dksih/QBM/2020/10/20/2575283505111040/2578114044436480/STEM/bda0f61dc51048a48acc9ddc2cca33e9.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a590a08b3823e01024de68e967cbf3f.png)
您最近一年使用:0次
名校
4 . 如图,已知点P在圆柱OO1的底面⊙O上,
分别为⊙O、⊙O1的直径,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/f41c80d5-edf3-4afa-8d8c-8c97af425e81.png?resizew=147)
(1)求证:
;
(2)若圆柱
的体积
,
①求三棱锥A1﹣APB的体积.
②在线段AP上是否存在一点M,使异面直线OM与
所成角的余弦值为
?若存在,请指出M的位置,并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d1d6aab81a6d708b1f7e8bbddf3085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/f41c80d5-edf3-4afa-8d8c-8c97af425e81.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865c39e73646d35cca68ce712e593bb4.png)
(2)若圆柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b38579913e81b3a06246a40a4990afb9.png)
①求三棱锥A1﹣APB的体积.
②在线段AP上是否存在一点M,使异面直线OM与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
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2019-06-19更新
|
405次组卷
|
2卷引用:【校级联考】福建省宁德市六校2018-2019学年高一下学期期中联考数学试题
5 . 如图,
中,
是
的中点,
,
.将
沿
折起,使
点与图中
点重合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63b2c21bd66fe36fd726d17a338fdda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef7d7abc808c38173ea94c60e098ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682481531576320/1689161281200128/STEM/60f1b52b6da84fa3975a1bce9579f4fd.png?resizew=17)
(Ⅰ)求证:;
(Ⅱ)当三棱锥的体积取最大时,求二面角
的余弦值;
(Ⅲ)在(Ⅱ)的条件下,试问在线段上是否存在一点
,使
与平面
所成的角的正弦值为
?证明你的结论.
![](https://img.xkw.com/dksih/QBM/2017/5/8/1682481531576320/1689161281200128/STEM/c656a068d94849ffbfdaca92a6e870f9.png?resizew=160)
您最近一年使用:0次
6 . 如图,在四棱锥
中,底面
是平行四边形,平面
底面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/42ebb8e166e64942a51ce2c67e100695.png)
(Ⅰ)求证:
平面
;
(Ⅱ)线段PC上是否存在一点F,使PA∥平面BDF?若存在,请找出具体位置,予以证明,并求点D到平面BCF的距离;若不存在,请分析说明理由.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/59127c2eea474658abc53372de71a9f6.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/5bccbc250538470a82ff8effe29abe57.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/82fcdda7fb1b432ca84cffb229ad3a28.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/5bccbc250538470a82ff8effe29abe57.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/7d210a0156eb4a4c9b3a54b880163dd6.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/214cac88675a4bac8001a1412423a41e.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/6a8c1c8769ef4e9a9e26ad0d6242b0cc.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/5578767f3cab4f568cb19c45e7bed9c7.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/42ebb8e166e64942a51ce2c67e100695.png)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/5c36c392eef24ff3a99ebe893f799005.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572959918194688/1572959924486144/STEM/5bccbc250538470a82ff8effe29abe57.png)
(Ⅱ)线段PC上是否存在一点F,使PA∥平面BDF?若存在,请找出具体位置,予以证明,并求点D到平面BCF的距离;若不存在,请分析说明理由.
您最近一年使用:0次
7 . 如图,四棱锥
中,底面
是正方形,
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
平面
;
(2)证明:平面
平面
.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d4c42112e0a22f240ce2ae432e5b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2018/5/5/1938553481633792/1940735921700864/STEM/53c9ec8cd2a7424b8c99ed8f8b79aa71.png?resizew=211)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-04更新
|
617次组卷
|
7卷引用:2015-2016学年福建省南安一中高一上学期期末考试数学试卷
名校
解题方法
8 . 如图,正方体
中,M,N,E,F分别是
,
,
,
的中点.
(2)求证:平面
平面EFDB;
(3)画出平面BNF与正方体侧面的交线
需要有必要的作图说明、保留作图痕迹,并说明理由
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46f725fb1c57d0855a0a6cc26bf562a.png)
(3)画出平面BNF与正方体侧面的交线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce08128582a7e855852c03e0ac5d0487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8c94316312f093ebfc80b872a83c25.png)
您最近一年使用:0次
名校
解题方法
9 . 如图(1),正三棱柱
,将其上底面ABC绕
的中心逆时针旋转
,
,分别连接
得到如图(2)的八面体
,依次连接该八面体侧棱
的中点分别为M,N,P,Q,R,S,
(ⅰ)求证:
共面;
(ⅱ)求多边形
的面积;
(2)求该八面体体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3a008a5ce2f3e0d93bf1b31f1e941d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b73c7e51c2fbe79faa78e5287d2ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff5cc57686ee7429fee0907651083c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff5cc57686ee7429fee0907651083c4.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ae231960760617a585b8478185d8ac.png)
(ⅱ)求多边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3662c929bd88085eb96dd4797482de.png)
(2)求该八面体体积的最大值.
您最近一年使用:0次
名校
解题方法
10 . 在通用技术课上,老师给同学们提供了一个如图所示的木质四棱锥模型
,
为正三角形,
,
,
为线段
的中点.
平面
;
(2)过点
的平面
交
于点
,沿平面
将木质四棱锥模型切割成两部分,在实施过程中为了方便切割,请你完成以下两件事情:
①在木料表面应该怎样画线?(在答题卡的图上画线要保留辅助线,并写出作图步骤);
②在木质四棱锥模型中确定
点的位置,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d94061dfdcef084c7594522ae9e512a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①在木料表面应该怎样画线?(在答题卡的图上画线要保留辅助线,并写出作图步骤);
②在木质四棱锥模型中确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8136c029f4b31e25c56c70a1432cbe1a.png)
您最近一年使用:0次