名校
解题方法
1 . 如图,三棱柱
中,D是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/03656881-a632-4480-aef3-10b67aaffd28.png?resizew=193)
(1)证明:
面
;
(2)若△
是边长为2的正三角形,且
,
,平面
平面
.求平面
与侧面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/03656881-a632-4480-aef3-10b67aaffd28.png?resizew=193)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad91719bd5fdc1b2d3d5298f2f44cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd426c9273efec5173db056d1d099f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
您最近一年使用:0次
2020-08-17更新
|
1717次组卷
|
7卷引用:辽宁省沈阳市第三十六中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
2 . 如图,四棱锥E﹣ABCD的侧棱DE与四棱锥F﹣ABCD的侧棱BF都与底面ABCD垂直,
,
//
,
.
![](https://img.xkw.com/dksih/QBM/2020/3/2/2410737436590080/2412398469545984/STEM/426907cc-7716-45c0-82c6-d9b05f14013e.png)
(1)证明:
//平面BCE.
(2)设平面ABF与平面CDF所成的二面角为θ,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.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/efdaef8d473c2deb6f4ca52e8fd9df0b.png)
![](https://img.xkw.com/dksih/QBM/2020/3/2/2410737436590080/2412398469545984/STEM/426907cc-7716-45c0-82c6-d9b05f14013e.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
(2)设平面ABF与平面CDF所成的二面角为θ,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5ff5a2e7663e6a21ccea3149a10113.png)
您最近一年使用:0次
2020-03-04更新
|
1221次组卷
|
7卷引用:辽宁省沈阳市第二中学2020届高三下学期第五次模拟考试数学(理)试题
3 . 如图所示的五面体
中,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
平面
,
,
,
∥
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/eed27dd5-5855-4aa4-ba45-fc2293db7059.png?resizew=160)
(Ⅰ)求证:
∥平面
;
(Ⅱ)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5427b7b994b860628df3d6b7a07de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d00572a90232e08932317af2a53767.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/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5441d73845911db1993bf903c4d8700f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/eed27dd5-5855-4aa4-ba45-fc2293db7059.png?resizew=160)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(Ⅱ)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
您最近一年使用:0次
2019-07-18更新
|
781次组卷
|
2卷引用:辽宁省六校协作体2019-2020学年高二上学期期中数学试题
4 . 如图,在三棱柱
中,
底面
,
,
,
,
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/e11707e5-9b2a-4c22-89d8-62716d4022b4.png?resizew=160)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3c5d2cbe5cfa47fde68ff3b5b81469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91c0da042c5af6c3540849bb686bc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9778ae9823e8430d73d87c57fc47b185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/e11707e5-9b2a-4c22-89d8-62716d4022b4.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca714e3eade6d63792b729f4ff9f8316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe033503db0cacc5ba9f9e97e74618.png)
您最近一年使用:0次
2019-01-16更新
|
889次组卷
|
4卷引用:【校级联考】辽宁省凌源2018-2019学年高二上学期期末三校联考数学(理科)试题
5 . 如图,在五面体ABCDEF中,点O是矩形ABCD的对角线的交点,面CDE是等边三角形,棱
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/565b9a7e-84cc-4f7d-8adb-8af0c745d2df.png?resizew=222)
(1)证明FO∥平面CDE;
(2)设BC=
CD,证明EO⊥平面CDE.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329d524fc86c714e064acf9bee9bc076.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/565b9a7e-84cc-4f7d-8adb-8af0c745d2df.png?resizew=222)
(1)证明FO∥平面CDE;
(2)设BC=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2019-09-20更新
|
352次组卷
|
3卷引用:辽宁省朝阳市建平县2018-2019学年高一下学期期末考试数学试卷
6 . 如图所示,已知正方体ABCD-A1B1C1D1.
![](https://img.xkw.com/dksih/QBM/2017/11/30/1828556743827456/1831479671291904/STEM/90469921-55bb-4af7-bcf7-8689db3aa233.png?resizew=233)
(1)求证:平面A1BD∥平面B1D1C.
(2)若E,F分别是AA1,CC1的中点,求证:平面EB1D1∥平面FBD.
![](https://img.xkw.com/dksih/QBM/2017/11/30/1828556743827456/1831479671291904/STEM/90469921-55bb-4af7-bcf7-8689db3aa233.png?resizew=233)
(1)求证:平面A1BD∥平面B1D1C.
(2)若E,F分别是AA1,CC1的中点,求证:平面EB1D1∥平面FBD.
您最近一年使用:0次
2017-12-05更新
|
1348次组卷
|
4卷引用:2015-2016学年辽宁省实验中学分校高一12月月考数学卷
2015-2016学年辽宁省实验中学分校高一12月月考数学卷人教A版高一年级必修二2.2.1直线与平面平行的判定数学试题(已下线)8.5 空间直线、平面的平行(已下线)第十三章 立体几何初步(知识归纳+题型突破)(2)-单元速记·巧练(苏教版2019必修第二册)
7 . 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)
您最近一年使用:0次
2016-12-03更新
|
6525次组卷
|
29卷引用:2015-2016学年辽宁省葫芦岛一中高一下期初摸底数学试卷
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
8 . 在三棱锥
中,平面
平面
,
,
,过
作
,垂足为
,点
,
分别是棱
,
的中点.
(
)求证:平面
平面
.
(
)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448cbac9a1ef3de7538a6b30cdc39582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd41dc960ba129a58f57cc8a92df32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee68c70ead4d3806540471a26925df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14913cb4acc97deaa4a34418a2dd2feb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc184dec8415d3f2e8e7ecfb452d690.png)
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219898564608/1809375470411776/STEM/b06bdf2e6e164ac69acefe49a2295cbe.png?resizew=227)
您最近一年使用:0次
2016-12-02更新
|
5362次组卷
|
16卷引用:辽宁省本溪市高一期末数学试题
(已下线)辽宁省本溪市高一期末数学试题辽宁省沈阳市郊联体2020-2021学年高一下学期期末考试数学试题辽宁省丹东市东港市第三中学2020-2021学年高一下学期期末数学试题2013年全国普通高等学校招生统一考试数学(江苏卷)2014-2015学年江苏省新丰中学高一下学期第二次学情调研数学试卷2015-2016学年湖南省邵阳市洞口一中高一上学期期末数学试卷北京市西城159中学2016-2017学年高二上学期期中考试数学试题人教A版高中数学必修二第二章 章末检测卷【全国百强校】安徽省太和中学2018-2019学年高一下学期第三次月考数学(文)试题陕西省西安电子科技大学附中2019-2020学年高一上学期第二次月考数学试题广西贺州市平桂高级中学2019-2020学年高一上学期期末考试数学试题吉林省长春市汽车经济技术开发区第六中学2020-2021学年第一学期高二月考数学(文)试题吉林省长春市汽车经济技术开发区第六中学2020-2021学年第一学期高二月考数学(理)试题福建省福州市闽江学院附属中学2020-2021学年高一6月月考数学试题广东省佛山市碧桂园学校2020-2021学年高二上学期期中数学试题广东省佛山市顺德区第一中学2019-2020学年高二上学期第一次阶段考试数学试题