名校
解题方法
1 . 如图,四棱锥
,平面
平面ABE,四边形ABCD为矩形,
,F为CE上的点,且
平面ACE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/7a282a40-dbf9-4ac0-9488-700f520b2271.jpg?resizew=178)
(1)求证:
;
(2)设M在线段DE上,且满足
,试在线段AB上确定一点N,使得
平面BCE,并求MN的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796e03af16c3b35ec4703c850a5035e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa3c61d6c19e187b4b824b6f5610cdb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/7a282a40-dbf9-4ac0-9488-700f520b2271.jpg?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48e31deb78dadacc7e128ef3eb2a054.png)
(2)设M在线段DE上,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b9be3999917b47890c1e763dd3f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
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2020-02-09更新
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5卷引用:江西省新余市2021届高三二模数学(文)试题
江西省新余市2021届高三二模数学(文)试题重庆市巴蜀中学2018-2019学年高二下学期期末考试数学(文)试题(已下线)专题8.6 翻折与探索性问题(精练)-2021年高考数学(文)一轮复习讲练测(已下线)专题8.6 翻折与探索性问题(精练)-2021年高考数学(文)一轮复习学与练(已下线)专题8.4 直线、平面平行的判定及性质(精讲)-2021年高考数学(理)一轮复习学与练
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2 . 如图所示,在四棱锥
中,底面
是边长为
的正方形,
平面
二面角
的大小为
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/fbbe7b72-05a9-480e-93cf-b17cbbee91b2.png?resizew=175)
(1)求证:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab69dcbdcd191102b0daf913c730055.png)
(2)在线段
上是否存在一点
,使得点
到平面
的距离为
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a955d5dab19e35c8e2a4437dae9e93f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe11ff2c080a2346c3a0f156ebaabd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee460fa5eec406f491e514ffd6285e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6241f9ef86cd0a902cbadaf336767dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6fec562d0b646ee75abe1cce5926d1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/fbbe7b72-05a9-480e-93cf-b17cbbee91b2.png?resizew=175)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cbe73724146a6ae435dc1fa7e88b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab69dcbdcd191102b0daf913c730055.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc704b98f4ed2c7359a7a5b6498b5290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23901e208d26f1332a51d26cedab4677.png)
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8卷引用:江西省吉安市第三中学2023届高三第一次模拟理科数学试题
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3 . 设
是两条不同的直线,
是两个不同的平面,则
的一个充分不必要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea0595c0c301a43c854a5dd1c548441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba83980a38c5e1fe4be841bc8a51d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516d9c67a3cef2ab0807e6faa4d49fa7.png)
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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3卷引用:【全国百强校】江西省新余四中、上高二中2019届高三第二次联考数学(文)试题
4 . 如图,在三棱柱
中,侧棱垂直于底面,
分别是
的中点.
(1)求证: 平面
平面
;
(2)求证:
平面
;
(3)求三棱锥
体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d646c02963c2bdf9b75686ba19e87a91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ea285e96bf2e3b6406151bb694f10a.png)
(1)求证: 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af12a8e26c1373c5a00e2011d3c613a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/7bc75e06-eaf5-400f-bd96-6146a5f0ee75.png?resizew=135)
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6526次组卷
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29卷引用:2020届江西名师联盟高三上学期第一次模拟考试数学(文)试题
2020届江西名师联盟高三上学期第一次模拟考试数学(文)试题2020届辽宁省葫芦岛市协作校、锦州市高三文科数学一模试题2014年全国普通高等学校招生统一考试文科数学(北京卷)(已下线)2015届广西桂林第十八中高三上学期第二次月考文科数学试卷2015-2016学年河南省郑州一中高一下期入学考试数学试卷2015-2016学年辽宁省葫芦岛一中高一下期初摸底数学试卷2016届山东省潍坊一中高三下学期起初考试文科数学试卷2016-2017学年黑龙江大庆一中高二上开学考数学试卷2016-2017学年山西怀仁一中高二文上学期月考三数学试卷天津市第一中学2017-2018学年高二上学期期中考试数学(文)试题2【校级联考】江苏省明德实验学校2018-2019学年高二上学期第二次学情调研(11月)数学试卷北京朝阳区陈经纶中学2017-2018学年高二上学期期中考试数学(文)试题【全国百强校】陕西省西安市长安区第一中学2018-2019学年高二上学期期末考试数学(文)试题【全国百强校】西藏自治区拉萨中学2019届高三第六次月考数学(文)试题安徽省滁州市定远县育才学校2019-2020学年高二(实验班)上学期第三次月考数学(文)试题宁夏吴忠中学2019-2020学年高二上学期期中考试数学(文)试题2020届辽宁省锦州市高三4月质量检测(一模)数学(文)试题安徽省滁州市定远县育才学校2020-2021学年高二上学期第一次月考数学(理)试题(已下线)【新东方】杭州新东方高中数学试卷339安徽省滁州市定远县民族中学2020-2021学年高二上学期10月月考数学(文)试题山西省阳泉市盂县第三中学2021届高三上学期第一次月考数学(文)试题宁夏吴忠中学2020-2021学年高二上学期期末考试数学(文)试题湖北省2020-2021学年高一下学期5月联考数学试题陕西省宝鸡市金台区2021-2022学年高一上学期期末数学试题贵州省毕节市赫章县2021-2022学年高二上学期期末教学质量监测数学(理)试题浙江省宁波市余姚中学2022-2023学年高一下学期期中数学试题(已下线)第11讲空间直线、平面的垂直(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(原卷版)北京十年真题专题07立体几何与空间向量(已下线)专题23 立体几何解答题(文科)-1
5 . 如图,在四棱锥
中,
为
上一点,面
面
,四边形
为矩形
,
,
.
(1)已知
,且
∥面
,求
的值;
(2)求证:
面
,并求点
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41130cc7adda7256e37caf3da3229109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58bbc02479917ad761a24eaae0dbfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5a0f84f14c15a0d4c2c912dcd01302.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12b081bc43f5bcc4f23a1d649fde7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0787d2cb66d00c49d3348b52acd407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://img.xkw.com/dksih/QBM/2014/6/4/1571755094605824/1571755100422144/STEM/d2c09a484c154275bdfe253da9a57fc4.png?resizew=240)
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3卷引用:2014届江西省重点中学盟校高三第二次联考文科数学试卷
(已下线)2014届江西省重点中学盟校高三第二次联考文科数学试卷江西省信丰中学2018-2019学年高二上学期第二次月考数学(理A+、A)试题【全国百强校】河南省南阳市第一中学2019届高三第十四次考试数学(文)试题
6 . 如图,四棱锥
的底面ABCD是平行四边形,
,
,
面
,设
为
中点,点
在线段
上且
.
(1)求证:
平面
;
(2)设二面角
的大小为
,若
,求
的长.
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/fbe2c93024cc4defbfd664d248c9f26b.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/dfbc51addab444a3a829a72863be52cd.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/882d788e0d574781b1594dc4601e5ec3.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/685c0c13d9b543ccb2abf857ba21f484.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/0f88a790965642b7bbd40dda123949cc.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/066cf30d2e9a4832ae21171d00faf2b5.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/31ca9d8f8e9b4da186f066541aa59eaf.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/29fd2392bfdb43eea30beb3d43441b56.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/17d0bfeb73964d6285dd9ccc81789d94.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/b3582d2246694bb6857ebdf05e0531a2.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/c61280d2722c4813b479568feb9fe407.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/d311c1e3123d4b8a80686aaf2c8c2b16.png)
(2)设二面角
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/8d05f983837848fa9266c355b68a62ec.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/deb1ec2b0dc944f5b9c7c266918e6e19.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/b391963284c348f493386694ee942773.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/47c7fdd31de043c5a115e358424e563a.png)
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571806394687488/1571806400512000/STEM/d69f2e43a8ea4c0b901632955bcc2ed9.png)
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