解题方法
1 . 在三棱柱
中,
,
.
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572146152660992/1572146158673920/STEM/1fe081c738744d72ae3d49853feef2df.png)
(Ⅰ)求证:
平面
;
(Ⅱ)若
,求证:
面
;
(Ⅲ)在(Ⅱ)的条件下,
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff212f4b2b6816427a84bb8fce0a8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b24c5dc15bb208eb05e897d8de110b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f5ab67eb430c9fcdf8e6b1a1744ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bb7488fc2656d8df3c52440daa3cff.png)
![](https://img.xkw.com/dksih/QBM/2015/6/25/1572146152660992/1572146158673920/STEM/1fe081c738744d72ae3d49853feef2df.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb4bda155f423bb67854a753b8058cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af254745c1c19bd20e83344bee674ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fbae62ef53e398a0e7276c97e7b888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(Ⅲ)在(Ⅱ)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908fdbef8613f4baaeb7524b84c07389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3caed541b28679bf596041c16401b6d4.png)
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2016-12-03更新
|
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2卷引用:2015届安徽省马鞍山市高中毕业班第三次质检文科数学试卷
2 . 五边形
是由一个梯形
与一个矩形
组成的,如图甲所示,B为AC的中点,
. 先沿着虚线
将五边形
折成直二面角
,如图乙所示.
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572110144913408/1572110150983680/STEM/880180fd-ce32-479a-b8e6-11723ee46c7a.png)
(Ⅰ)求证:平面
平面
;
(Ⅱ)求图乙中的多面体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf91800a153de7cef135199c362c8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61730fa803f228256cd9ce55802b565b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe3afb7faf71778e09104887da51a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf91800a153de7cef135199c362c8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cbb74984939d59964559c3560ef7ba.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572110144913408/1572110150983680/STEM/880180fd-ce32-479a-b8e6-11723ee46c7a.png)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b61cb6f9db386066ddf8f9d57e4f705f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf1e1b7ad2c64592e17b9500afbc28.png)
(Ⅱ)求图乙中的多面体的体积.
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2卷引用: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
解题方法
3 . 如图,已知四边形
和
都是菱形,平面
和平面
互相垂直,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf318fa9d6cfb50669b3d57f462e833.png)
![](https://img.xkw.com/dksih/QBM/2015/4/29/1572084211834880/1572084217610240/STEM/d694a15e4b774df6a3692a080bad5971.png?resizew=314)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05069ea91c2edfcafd085b3d2a25fd95.png)
(2)求四面体
的体积;
(3)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf318fa9d6cfb50669b3d57f462e833.png)
![](https://img.xkw.com/dksih/QBM/2015/4/29/1572084211834880/1572084217610240/STEM/d694a15e4b774df6a3692a080bad5971.png?resizew=314)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05069ea91c2edfcafd085b3d2a25fd95.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c101cf014b5c61662b6446484d45f0bf.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0715b04d494f97e6efe2ff694388c73.png)
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4 . 一个多面体的直观图及三视图如图所示,其中M ,N 分别是AF、BC 的中点
![](https://img.xkw.com/dksih/QBM/2014/10/29/1571886148894720/1571886154792960/STEM/a77c450c59f249239986553260b6d687.png)
![](https://img.xkw.com/dksih/QBM/2014/10/29/1571886148894720/1571886154792960/STEM/df3192271f5d4710b41cea266ece3239.png)
(1)求证:MN∥平面CDEF;
(2)求多面体A-CDEF的体积.
![](https://img.xkw.com/dksih/QBM/2014/10/29/1571886148894720/1571886154792960/STEM/a77c450c59f249239986553260b6d687.png)
![](https://img.xkw.com/dksih/QBM/2014/10/29/1571886148894720/1571886154792960/STEM/df3192271f5d4710b41cea266ece3239.png)
(1)求证:MN∥平面CDEF;
(2)求多面体A-CDEF的体积.
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4卷引用:安徽省宣城二中2020-2021学年高二上学期开学考试理科数学试题
安徽省宣城二中2020-2021学年高二上学期开学考试理科数学试题(已下线)2015届吉林省吉林市高三第一次摸底考试文科数学试卷宁夏回族自治区银川一中2020届高三第四次模拟考试数学(文)试题甘肃省兰州市第一中学2019-2020学年高二下学期期末考试数学试题
5 . 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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29卷引用: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
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(已下线)【新东方】杭州新东方高中数学试卷339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
11-12高三·河北石家庄·阶段练习
名校
解题方法
6 . 如图,在三棱柱
中,
⊥
,
⊥
,
,
为
的中点,且
⊥
.
![](https://img.xkw.com/dksih/QBM/2012/9/5/1571000268152832/1571000273502208/STEM/5883c312924f44a7a5c937a25eb07b12.png)
(1)求证:
⊥平面
;(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f32f651907d6c9001655481f79ebda84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
![](https://img.xkw.com/dksih/QBM/2012/9/5/1571000268152832/1571000273502208/STEM/5883c312924f44a7a5c937a25eb07b12.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee77a25408ab2bfb1ab57db67359332.png)
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2016-12-01更新
|
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5卷引用:安徽省黄山市屯溪第一中学2022届高三上学期10月月考文科数学试题
安徽省黄山市屯溪第一中学2022届高三上学期10月月考文科数学试题安徽省安庆市重点高中2022届高三上学期10月月考文科数学试题(已下线)2012届河北省正定中学高三第二次综合考试文科数学试卷2016届云南省玉溪市一中高三上学期期中文科数学试卷2020届甘肃省天水市第一中学等八校联考高三12月联考数学(文)试题
2012·安徽安庆·二模
解题方法
7 . 如图,几何体ABC-EFD是由直三棱柱截得的,EF //AB,∠ABC=90°,AC=2AB =2,CD=2AE=
,
(I)求三棱锥D-BEC的体积;
(I I)求证:CE⊥DB
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
(I)求三棱锥D-BEC的体积;
(I I)求证:CE⊥DB
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/15/cb01d1c9-e51f-4f26-b0de-c90a0e7e7c31.png?resizew=142)
您最近一年使用:0次
2012·湖北襄阳·一模
名校
8 . 如图,三棱台
的底面是正三角形,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2012/3/14/1570802134179840/1570802139783168/STEM/55bec17d-1890-42ff-b8e1-a8313647fb49.png?resizew=191)
(Ⅰ)求证:
;
(Ⅱ)若
和梯形
的面积都等于
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45378fbdfb5fe305c71893a91435854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616b46476c1f1d22e3a21d6fa33a3400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc335e69ac1151ff812921e9a8f2ec37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf5b86308e9f777a6611503ba8d0e9e.png)
![](https://img.xkw.com/dksih/QBM/2012/3/14/1570802134179840/1570802139783168/STEM/55bec17d-1890-42ff-b8e1-a8313647fb49.png?resizew=191)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc0666d63e6c13fa6a19b59523aa1eb.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616b46476c1f1d22e3a21d6fa33a3400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661f3d965e8c6043e3d1cd5dbc270270.png)
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9卷引用:【市级联考】安徽省合肥市2019届高三第二次教学质量检测数学(文)试题
【市级联考】安徽省合肥市2019届高三第二次教学质量检测数学(文)试题安徽省合肥市巢湖市四中2019-2020学年高二上学期第四次月考数学试题(已下线)2012届湖北省襄阳市高三3月调研考试数学理科试卷【全国百强校】江西省南昌市第二中学2018-2019学年高二下学期第一次月考数学(文)试题四川省遂宁二中2018-2019学年高二下学期期中考试数学(文)试题2019年9月广东省梅州市高三上学期第一次质量检测数学(文)试题广东省广州市执信中学2018-2019学年高二下学期期中数学(文)试题四川省仁寿第二中学2020届高三第三次高考模拟数学(文)试题四川省泸州市泸县第一中学2021-2022学年高三三诊模拟考试文科数学试题
9 . 如图,在六面体
中,平面
平面
,
平面
,
平面
,
,且
,
.
![](https://img.xkw.com/dksih/QBM/2011/12/22/1570628813758464/1570628819214336/STEM/f9a6d72fbf6543bfb89a677329cb85ee.png?resizew=171)
(1)求证:平面
平面
;
(2)求证:
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e38a1b5cfffd43a3405481a1d67cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/617edf7f259f5955db7cad814af85281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9beeedb7ddaac2cd3d37151d058ab7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f383b759b5207e29698e93ed86216a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd6ae694a4678178afc4439cc7608f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151b7172db8b4af240ef0439778d792c.png)
![](https://img.xkw.com/dksih/QBM/2011/12/22/1570628813758464/1570628819214336/STEM/f9a6d72fbf6543bfb89a677329cb85ee.png?resizew=171)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3df0d9a6c83b35a863544a01f22ef7.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26712d1a7a5864cd18498f16f7bd96c.png)
您最近一年使用:0次
2011·江苏宿迁·二模
解题方法
10 . 如图,在棱长为2的正方体
中,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2011/3/17/1570046058397696/1570046063738880/STEM/442e0326-c9ce-49d7-bef7-2ca31929c477.png?resizew=180)
(1)求证:
平面
;
(2)求证:
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b866a756d422faec0f7eb229dfaabf.png)
![](https://img.xkw.com/dksih/QBM/2011/3/17/1570046058397696/1570046063738880/STEM/442e0326-c9ce-49d7-bef7-2ca31929c477.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3d48dafb6b017b5739106c1b88be7ee.png)
您最近一年使用:0次
2016-11-30更新
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978次组卷
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