1 . 如图,四棱锥
,侧面
是边长为
的正三角形,且与底面垂直,底面
是
的菱形,
为
的中点.
(1)求证:
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051f092cbf89536d7e8b9fbf9d49355d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d85caf2bd9c6c66709d09df0ee0ac.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745df4f226027778d5fe45b6501b822.png)
![](https://img.xkw.com/dksih/QBM/2017/5/17/1689146393174016/1689201675509760/STEM/02c33f918e184aedb723f2984dd0e630.png?resizew=231)
您最近一年使用:0次
2016-12-03更新
|
1530次组卷
|
7卷引用:2015届吉林省实验中学高三上学期第五次模拟考试文科数学试卷
11-12高二上·浙江杭州·期末
2 . 如图,在三棱柱
中,
侧面
,已知
,
,
.
![](https://img.xkw.com/dksih/QBM/2012/7/16/1570926421106688/1570926426349568/STEM/e4033190d0664822978de2c67382f98f.png?resizew=230)
(1)求证:
平面
;
(2)试在棱
(不包含端点
上确定一点
的位置,使得
;
(3)在(2)的条件下,求二面角
的平面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98daab2b277b67e14454772d3e0d3fd.png)
![](https://img.xkw.com/dksih/QBM/2012/7/16/1570926421106688/1570926426349568/STEM/e4033190d0664822978de2c67382f98f.png?resizew=230)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ad7c180d6d084ecb25f23cb6fe9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)试在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e5090124abbafa4601c9b7b2c942c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7fda523ada8989e466d797b6fcd2e0.png)
(3)在(2)的条件下,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69cbd2557ef69775b5a883c510091985.png)
您最近一年使用:0次
真题
名校
3 . 如图,在四棱锥
中,
平面
,底面
是菱形,
,
.
![](https://img.xkw.com/dksih/QBM/2018/6/25/1975123199098880/2009033766846464/STEM/081dd6d66c6140d8b2c56f6059ecc712.png?resizew=201)
(
)求证:
平面
.
(
)若
,求
与
所成角的余弦值.
(
)当平面
与平面
垂直时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://img.xkw.com/dksih/QBM/2018/6/25/1975123199098880/2009033766846464/STEM/081dd6d66c6140d8b2c56f6059ecc712.png?resizew=201)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
您最近一年使用:0次
2016-11-30更新
|
3524次组卷
|
11卷引用:2011-2012学年吉林省吉林一中高二上学期质量检测理科数学
(已下线)2011-2012学年吉林省吉林一中高二上学期质量检测理科数学2011年普通高中招生考试北京市高考理科数学(已下线)2011-2012学年山东省济宁市鱼台二中高二上学期期末考试理科数学(已下线)2013-2014学年河北衡水中学高二上第四次调研考试理数学卷2015届福建省三明市一中高三上学期第二次月考理科数学试卷2015-2016学年四川省成都七中实验学校高二上学期期中文科数学试卷河北省武邑中学2017届高三下学期一模考试数学(理)试题北京市石景山第九中学2017-2018高二上期中试卷 北师大版 数学(理科)上海市普陀区曹杨二中2017-2018学年度高二上学期12月月考数学试题人教B版(2019) 选择性必修第一册 过关斩将 第一章 空间向量与立体几何 1.2 空间向量在立体几何中的应用 1.2.2 空间中的平面与空间向量陕西省咸阳市实验中学2020-2021学年高二上学期第三次月考数学(理)试题
2010·吉林·模拟预测
4 . 如图,在直三棱柱
中,
,
是棱
上的动点,
是
中点,
,
.
![](https://img.xkw.com/dksih/QBM/2015/12/14/1572355636092928/1572355641778176/STEM/8e9eecba6513410482e450e02f26ebf4.png)
(Ⅰ)求证:
平面
;
(Ⅱ)若二面角
的大小是
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405d4e4b1755e82269bb95b1e1a44d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/12/14/1572355636092928/1572355641778176/STEM/a5a6e77feb5e473ab2b2ce89b4d4f7e3.png)
![](https://img.xkw.com/dksih/QBM/2015/12/14/1572355636092928/1572355641778176/STEM/66682a872f674602a8b3e63452f21cee.png)
![](https://img.xkw.com/dksih/QBM/2015/12/14/1572355636092928/1572355641778176/STEM/8e9eecba6513410482e450e02f26ebf4.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f11e5b3ebac5f333e53ba46fb88f7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
(Ⅱ)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c09b75b6951958234d879ac6d4d7bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6fdfbf0ea031149dd4a8f8235fae73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
您最近一年使用:0次
5 . 如图,长方体
中,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/22759c45bb6d4ea096ae8bc38c0f7de1.png)
(1)求证:直线
∥平面
;
(2)求证:平面![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/6d12fbc5e916426bb67f7267cc80a2bd.png)
平面
;
(3)求证:直线![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/ef40f6a3dc374c07aae0217dce1b4da3.png)
平面
.
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/5b2fb361a31a4516ae2e03e84c0baa30.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/3d9981b93bca4354acf1162f81c66992.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/7d1504a55c154bf3a99275ab9715f1dc.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/3b56de4c9c344aa1b0c39c7fee40124c.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/9f3d22d3d1a147e39aa623b8535aa6aa.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/22759c45bb6d4ea096ae8bc38c0f7de1.png)
(1)求证:直线
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/f214e4ffb71f448c9e5b47e75c41eb4f.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/6d12fbc5e916426bb67f7267cc80a2bd.png)
(2)求证:平面
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/6d12fbc5e916426bb67f7267cc80a2bd.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/0796148345294334b0906da905790296.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/ce242d31db184c66bb56c4f8db657a58.png)
(3)求证:直线
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/ef40f6a3dc374c07aae0217dce1b4da3.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/0796148345294334b0906da905790296.png)
![](https://img.xkw.com/dksih/QBM/2013/1/24/1571107409387520/1571107414958080/STEM/6d12fbc5e916426bb67f7267cc80a2bd.png)
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6 . 在如图所示的几何体中,D是AC的中点,EF∥DB.
(Ⅰ)已知AB=BC,AE=EC.求证:AC⊥FB;
(Ⅱ)已知G,H分别是EC和FB的中点.求证:GH∥平面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/2ef50c17-3807-43c3-99e9-243e47d85f07.png?resizew=130)
(Ⅰ)已知AB=BC,AE=EC.求证:AC⊥FB;
(Ⅱ)已知G,H分别是EC和FB的中点.求证:GH∥平面ABC.
您最近一年使用:0次
2016-12-04更新
|
1084次组卷
|
14卷引用:吉林省辽源市田家炳高级中学(六十七届友好学校)2018-2019学年高一下学期期末联考数学(理)试题
吉林省辽源市田家炳高级中学(六十七届友好学校)2018-2019学年高一下学期期末联考数学(理)试题吉林省辽源市田家炳高级中学(六十七届友好学校)2018-2019学年高一下学期期末联考数学(文)试题2016年全国普通高等学校招生统一考试文科数学(山东卷精编版)安徽省合肥市第一中学2017-2018学年高二上学期段一考试(月考)数学(文)试题人教A版高中数学必修二 2.3.1直线与平面垂直的判定3安徽省合肥市第一中学2017-2018学年高二上学期月考文数试题【校级联考】四川省南充市南部县五校2017-2018学年高一下学期期末考试数学试题湖南省岳阳市平江县第一中学2020-2021学年高三上学期11月月考数学试题四川省凉山州民族中学2021-2022学年高二上学期入学摸底考试数学(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(已下线)2016年全国普通高等学校招生统一考试文科数学(山东卷参考版)北京名校2023届高三一轮总复习 第8章 立体几何 8.2 空间中平行关系的判定及其性质(已下线)专题23 立体几何解答题(文科)-1专题32立体几何与空间向量解答题(第二部分)
2014·吉林长春·一模
解题方法
7 . 如图所示几何体是正方体
截去三棱锥
后所得,点
为
的中点.
(1) 求证:
平面
;
(2) 当正方体棱长等于
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8456cee87c4e22351affc28f3a73a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a03c218ad44c5138efface5b2ed903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
(1) 求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d254c1fe8900cf54457d5888c01734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(2) 当正方体棱长等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dceaf76fc1199b3cc5aa0f569dd38f.png)
![](https://img.xkw.com/dksih/QBM/2014/9/26/1571864175566848/1571864181063680/STEM/1f05802dd8794e558acb67cb34b01f6a.png)
您最近一年使用:0次
13-14高二·江苏扬州·阶段练习
名校
8 . 如图所示,在四棱锥P—ABCD中,底面ABCD是矩形,侧棱PA垂直于底面,E、F分别是AB、PC的中点,PA=AD.
![](https://img.xkw.com/dksih/QBM/2014/9/26/1571863340064768/1571863345389568/STEM/85739ab4cc044951a3a2d0be89bf3135.png)
求证:(1)CD⊥PD;(2)EF⊥平面PCD.
![](https://img.xkw.com/dksih/QBM/2014/9/26/1571863340064768/1571863345389568/STEM/85739ab4cc044951a3a2d0be89bf3135.png)
求证:(1)CD⊥PD;(2)EF⊥平面PCD.
您最近一年使用:0次
2016-12-03更新
|
1354次组卷
|
5卷引用:吉林省吉林市吉化一中2019-2020学年高一上学期第二次月考数学试题
9 . 圆锥
如图①所示,图②是它的正(主)视图.已知圆
的直径为
,
是圆周上异于
,
的一点,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2019/4/15/2183007787024384/2184241760206848/STEM/514b3c2ef1194d98957e468546a80d50.png?resizew=276)
(1)求该圆锥的侧面积
;
(2)求证:平面
平面
;
(3)若
,在三棱锥
中,求点A到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2019/4/15/2183007787024384/2184241760206848/STEM/514b3c2ef1194d98957e468546a80d50.png?resizew=276)
(1)求该圆锥的侧面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15b63176f43bc7a0654d0f6f45e7429.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c646c683fbe522edb7ea54fd3ad873d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2016-12-02更新
|
2201次组卷
|
5卷引用:吉林省吉林市实验中学2019届高三下学期第八次月考数学(文)试题