解题方法
1 . 如图,在直三棱柱
中,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2015/12/29/1572405501837312/1572405507850240/STEM/b69270086ffa49a0b7cd6f6dc92bc7f7.png?resizew=147)
(1)求证:
∥平面
;
(2)若
,
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2015/12/29/1572405501837312/1572405507850240/STEM/b69270086ffa49a0b7cd6f6dc92bc7f7.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97abea909791f73b84a07d3f15d8535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
您最近一年使用:0次
2016-12-03更新
|
448次组卷
|
3卷引用:【全国市级联考】海南省琼海市2018届高考模拟考试文数试卷
2 . 如图,在四棱锥
中,底面
是菱形,
,
平面
,
,点
,
分别为
和
中点.
![](https://img.xkw.com/dksih/QBM/2019/6/7/2220421574721536/2220564689354752/STEM/94fa724f5a704273a11ad9a2198f007a.png?resizew=112)
(1)求证:直线
平面
;
(2)求
与平面
所成角的正弦值.
![](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/ea4f5eec0addba78f2e0cdfb7ecc59a6.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/b624742fe28db114e0554c6c87bff05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2019/6/7/2220421574721536/2220564689354752/STEM/94fa724f5a704273a11ad9a2198f007a.png?resizew=112)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2016-12-03更新
|
1846次组卷
|
11卷引用:海南省华中师范大学琼中附属中学2020-2021学年高二上学期期中考试数学试题
海南省华中师范大学琼中附属中学2020-2021学年高二上学期期中考试数学试题2015届吉林省长春市普通高中高三质量监测三理科数学试卷2014-2015学年浙江省台州中学高二下学期第一次统练文科数学试卷【全国省级联考】黑龙江省2018年普通高等学校招生全国统一考试仿真模拟(二)数学(理科)试题【全国百强校】山西省临汾市临汾一中2018-2019学年高二下学期期中数学试题(理)上海市普陀区2018-2019学年高三上学期期中阶段测试数学试题2019年上海市普陀区高三上学期期末统考数学试题重庆市江津中学、合川中学等七校2019-2020学年高三第三次诊断性考试数学(理)试题2019届重庆市江津中学、合川中学等七校高三第三次诊断性考试(理科)数学试题江苏省镇江市八校2020-2021学年高三上学期期中联考数学试题浙江省2021届高三高考数学预测卷(二)
11-12高二下·北京·期中
3 . 如图,三棱柱
中,
⊥平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2015/9/23/1572239377891328/1572239383977984/STEM/477065a330894238adb68aa9ea750e5a.png?resizew=192)
(Ⅰ)求证:
平面
;
(Ⅱ)求二面角
的余弦值;
(Ⅲ)在侧棱
上是否存在点
,使得
平面
?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283c8668ca30b171ee4352452e1c7e94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.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/2015/9/23/1572239377891328/1572239383977984/STEM/477065a330894238adb68aa9ea750e5a.png?resizew=192)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1496afecd92a619fbe5e9b736f06f4e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd190b5a26dfb45a06c1d6ee86dd82d9.png)
(Ⅲ)在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e245440d3761fb4217eaa8dc303fa288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
您最近一年使用:0次
2014高三·全国·专题练习
解题方法
4 . 如图,在四棱锥PABCD中,PA⊥底面ABCD,PC⊥AD,底面ABCD为梯形,AB∥DC,AB⊥BC,PA=AB=BC,点E在棱PB上,且PE=2EB.
![](https://img.xkw.com/dksih/QBM/2014/3/18/1571568675348480/1571568680173568/STEM/9d118bea142e4723925dc631ce976f61.png)
(1)求证:平面PAB⊥平面PCB;
(2)求证:PD∥平面EAC.
![](https://img.xkw.com/dksih/QBM/2014/3/18/1571568675348480/1571568680173568/STEM/9d118bea142e4723925dc631ce976f61.png)
(1)求证:平面PAB⊥平面PCB;
(2)求证:PD∥平面EAC.
您最近一年使用:0次
12-13高二下·甘肃天水·期末
5 . 如图,在三棱锥P-ABC中,PA=PB=AB=2,BC=3,∠ABC=90°,平面PAB⊥平面ABC,D、E分别为AB、AC中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/1/726dd93d-b665-4005-a50f-5173822377c7.png?resizew=194)
(1)求证:
平面PBC;
(2)求证:AB⊥PE;
(3)求二面角A-PB-E的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/1/726dd93d-b665-4005-a50f-5173822377c7.png?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7440b41636c761b0910639e310ff7dfb.png)
(2)求证:AB⊥PE;
(3)求二面角A-PB-E的大小.
您最近一年使用:0次
2016-12-02更新
|
1904次组卷
|
5卷引用:2015-2016学年海南省文昌中学高二上期末理科数学试卷
2015-2016学年海南省文昌中学高二上期末理科数学试卷(已下线)2012-2013学年甘肃天水一中高二下学期期末考试理科数学试卷(已下线)2014届湖南省益阳市箴言中学高三第一次模拟考试理数学试卷2017届甘肃肃南裕固族自治县一中高三理10月月考数学试卷2017届甘肃肃南裕固族自治县一中高三文10月月考数学试卷
13-14高三上·吉林·期末
6 . 如图,四棱锥P-ABCD中,底面ABCD是平行四边形,∠ACB=90°,平面PAD⊥平面ABCD,
PA=BC=1,PD=AB=
,E、F分别为线段PD和BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/df27b151-02a1-467e-9489-8358334c7e38.png?resizew=223)
(Ⅰ) 求证:CE∥平面PAF;
(Ⅱ)在线段BC上是否存在一点G,使得平面PAG和平面PGC所成二面角的大小为60°?若存在,试确定G的位置;若不存在,请说明理由.
PA=BC=1,PD=AB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7881094ce2f907c3aaf664318ecd3e2d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/13/df27b151-02a1-467e-9489-8358334c7e38.png?resizew=223)
(Ⅰ) 求证:CE∥平面PAF;
(Ⅱ)在线段BC上是否存在一点G,使得平面PAG和平面PGC所成二面角的大小为60°?若存在,试确定G的位置;若不存在,请说明理由.
您最近一年使用:0次
2016-12-02更新
|
1080次组卷
|
6卷引用:2013届海南省琼海市嘉积中学高三下学期第一次月考理科数学试卷
(已下线)2013届海南省琼海市嘉积中学高三下学期第一次月考理科数学试卷(已下线)2013届吉林省吉林市普通中学高三上学期期末考试理科数学试卷2015-2016学年河北省正定中学高二上学期期末理科数学卷云南省昆明市官渡区2021届高三上学期两校联考数学试题(已下线)热点09 立体几何-2021年高考数学【热点·重点·难点】专练(新高考)宁夏银川三沙源上游学校2020-2021学年高二下学期第一次月考数学(理)试题
11-12高三·山东临沂·阶段练习
解题方法
7 . 如图所示,四棱锥
中,
为正方形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351ca06b70fa7e8fca506e3a453e9450.png)
分别是线段
的中点. 求证:
(1)
//平面
;
(2)平面
⊥平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6153163fecdf3f410411048428ccaef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351ca06b70fa7e8fca506e3a453e9450.png)
![](https://img.xkw.com/dksih/QBM/2013/1/22/1571106006917120/1571106012512256/STEM/84c7a0486c544123a18946ebf29af85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556d12499fdd98643afc5f45ea678d2.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://img.xkw.com/dksih/QBM/2013/1/22/1571106006917120/1571106012512256/STEM/276af8d8eb57488c8019df05929e5bcf.png)
![](https://img.xkw.com/dksih/QBM/2013/1/22/1571106006917120/1571106012512256/STEM/3c69ce6bd3834c83a18ffa012657216c.png)
您最近一年使用:0次
12-13高三上·海南省直辖县级单位·期末
8 . 如图,四棱锥
中,底面
为矩形,
底面
,且
,
,点
是
中点
![](https://img.xkw.com/dksih/QBM/2012/2/16/1570743170301952/1570743175880704/STEM/97d3631d-9f28-49c3-bc06-2cffa493dd04.png?resizew=179)
(Ⅰ)若
为
中点,证明:
//平面
;
(Ⅱ)若
是
边上任一点,证明:
;
(Ⅲ)若
,求直线
与平面
所成角的正弦值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2012/2/16/1570743170301952/1570743175880704/STEM/97d3631d-9f28-49c3-bc06-2cffa493dd04.png?resizew=179)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a395778dcf588264f40e1cd8c96206d.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9e036eecc9aebcc2d2a2855bbfafdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
您最近一年使用:0次
9 . 如图中,是一个长方体截去一个角所得多面体的直观图.它的正视图和侧视图在右面画出(单位:cm).
(1)在正视图下面,按照画三视图的要求画出该多面体的俯视图;
(2)按照给出的尺寸,求该多面体的体积;
(3)在所给直观图中连接BC′,证明:BC′∥面EFG.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/9f850028-6734-42b5-9029-6446d708977d.png?resizew=148)
(1)在正视图下面,按照画三视图的要求画出该多面体的俯视图;
(2)按照给出的尺寸,求该多面体的体积;
(3)在所给直观图中连接BC′,证明:BC′∥面EFG.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/9f850028-6734-42b5-9029-6446d708977d.png?resizew=148)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/0acf4731-10cc-4465-8855-f85547c1908f.png?resizew=186)
您最近一年使用:0次
2016-12-01更新
|
963次组卷
|
6卷引用:2008年普通高等学校招生考试数学(文)试题(琼、宁卷)
2008年普通高等学校招生考试数学(文)试题(琼、宁卷)(已下线)2011年福建省南安一中高一上学期期末考试数学试卷(已下线)2011-2012年广东省台山侨中高一上学期第二次月考试题数学2016-2017汕头潮阳实验学校高二培优班8月月考数学试卷陕西省西安交通大学附属中学雁塔校区2022-2023学年高三下学期高考模拟数学试题陕西省西安交通大学第二附属中学2022届高三下学期第三次月考理科数学试题
2011高一上·海南·学业考试
解题方法
10 . 已知四棱锥P-ABCD,底面ABCD是
,边长为a的菱形,又PA⊥平面ABCD,且PD=CD,点M、N分别是棱AD、PC的中点.
(1)证明:DN//平面PMB;
(2)求DN与MB所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a6f36741b86f464be362b12bac13d2.png)
(1)证明:DN//平面PMB;
(2)求DN与MB所成的角的正弦值.
![](https://img.xkw.com/dksih/QBM/2011/12/16/1570620058009600/1570620063260672/STEM/1bb4dd5f1ba049c4855a294f1cb470e8.png?resizew=220)
您最近一年使用:0次