1 . 如图,ABCD是块矩形硬纸板,其中AB=2AD,AD=
,E为DC的中点,将它沿AE折成直二面角D-AE-B.
![](https://img.xkw.com/dksih/QBM/2016/3/22/1572553729376256/1572553735413760/STEM/45313a1eefc1407badfc7615c651e5ae.png)
(1)求证:AD⊥平面BDE;
(2)求二面角B-AD-E的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2016/3/22/1572553729376256/1572553735413760/STEM/45313a1eefc1407badfc7615c651e5ae.png)
(1)求证:AD⊥平面BDE;
(2)求二面角B-AD-E的余弦值.
您最近一年使用:0次
2016-12-04更新
|
498次组卷
|
2卷引用:2016-2017学年广东省仲元中学高二上学期期末考试数学(理)试卷
2 . 在正三棱锥
中,
、
分别为棱
、
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/2ba52750b4c54f94a53a9e5ead3d1cd2.png)
(1)求证:直线
平面
;
(2)求证:平面
平面
.
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/06a1a2bd819a44c982a525ad6cde88df.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/31e6e0f27e9e48be86cebe33864a9223.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/41469a49c14b4de586c547ff8df8bc98.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/940335b942964da888138fc6690f4f5a.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/960ff362f8da4645bd3dcf59ad26abee.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/b106e917b59340c384ebd38015c24826.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/2ba52750b4c54f94a53a9e5ead3d1cd2.png)
(1)求证:直线
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/f38c6affd7034c46b6e7384380ce8c91.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/34c371fb18144b0ba07dda89b61665c3.png)
(2)求证:平面
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/0721aeca5f464bd3ac7c553fde9eb777.png)
![](https://img.xkw.com/dksih/QBM/2015/9/11/1572229475041280/1572229480955904/STEM/f29f0ced562b4449b8ecd08a228540fe.png)
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3 . 已知平行四边形
,
,
,
,
为
的中点,把三角形
沿
折起至
位置,使得
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572037567160320/1572037572517888/STEM/cdb7ec85fe5c4e65804133d4ebbc3ceb.png)
(1)求证:
;
(2)求证:面
面
;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e1d24e6954a9736aa6ed412fa43bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502fc5e3c7f636aac9064ec69018c95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://img.xkw.com/dksih/QBM/2015/3/26/1572037567160320/1572037572517888/STEM/cdb7ec85fe5c4e65804133d4ebbc3ceb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ab1af4b3c939b0b1f819e831e32e0.png)
(2)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83716c0f110a635037adbffc7bbbb183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483f030abf61c6a0882d656d63cf4512.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516dfcfba39af76a6fffa94ac307f581.png)
您最近一年使用:0次
11-12高二·广东·阶段练习
名校
解题方法
4 . 如图所示,在棱长为2的正方体
中,
、
分别为
、
的中点.
(Ⅰ)求证:
//平面
;
(Ⅱ)求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d435974639ea2850bb5c21efe64b123b.png)
![](https://img.xkw.com/dksih/QBM/2012/2/17/1570744981004288/1570744986304512/STEM/d5f71ea2-bc73-4b2c-b2c8-9b82da5fd984.png?resizew=170)
您最近一年使用:0次
10-11高一下·黑龙江牡丹江·期末
名校
5 . 如图,四棱锥P-ABCD中,底面ABCD为平行四边形,∠DAB=60°,AB=2AD,PD⊥底面ABCD.
(2)若PD=AD,求二面角A-PB-C的余弦值.
(2)若PD=AD,求二面角A-PB-C的余弦值.
您最近一年使用:0次
2016-12-03更新
|
3747次组卷
|
32卷引用:2015届广东省惠州市高三第二次调研考试理科数学试卷
(已下线)2015届广东省惠州市高三第二次调研考试理科数学试卷(已下线)2015届广东省惠州市高三第二次调研考试理科数学试卷(已下线)黑龙江省牡丹江一中10-11学年高一下学期期末考试数学(理)(已下线)2012-2013学年黑龙江哈尔滨第十二中学高二上期末考试理科数学卷(已下线)2013届甘肃省甘谷四中度高二下学期第二次检测考试理科数学试卷2015届山西省大同、同煤一中高三上学期期末考试理科数学试卷2016届黑龙江大庆实验中学高三考前训练一理科数学试卷贵州省思南中学2016-2017学年高二下学期期末考试数学(理)试题广西南宁市马山县金伦中学2016-2017学年高二下学期期末考试数学(理)试题陕西省黄陵中学2018-2019学年高二上学期期末考试数学(理)试题【全国百强校】湖南省衡阳市第一中学2018-2019学年高二下学期期中考试数学(理)试题【全国百强校】内蒙古集宁一中(西校区)2018-2019学年高二6月月考数学(理)试题福建省南平市建瓯市芝华中学2019-2020学年高二上学期期中数学试题2018届西藏自治区拉萨中学高三第六次月考数学(理)试题湖南省怀化市2018-2019学年高二下学期期末数学(理)试题广西桂林市临桂区两江中学2019-2020学年高二下学期第二次月考数学(理)试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)云南省玉龙纳西族自治县田家炳民族中学2019-2020学年高二下学期期中考试数学(理)试题(已下线)【新教材精创】1.2.4+二面角(1)A基础练-人教B版高中数学选择性必修第一册云南省保山市第九中学2021届高三第三次月考数学(理)试题云南省保山市第九中学2021届高三第三次月考数学(文)试题(已下线)易错点10 立体几何中的角-备战2021年高考数学(理)一轮复习易错题新疆乌苏市第一中学2020-2021学年高二(4-27班)下学期入学检测数学试题河北省张家口市第一中学2021-2022学年高二上学期10月月考数学试题江苏省南京市第五中学2021-2022学年高三上学期10月月考数学试题(已下线)9.5 空间向量与立体几何(已下线)专题06 求空间角妙招迭出,施向量法更添风采广西玉林市田家炳中学2015-2016学年高二1月月考数学试题(已下线)专题24 空间向量与空间角的计算-十年(2011-2020)高考真题数学分项宁夏石嘴山市平罗中学2024届高三上学期第一次月考数学(理)试题(A)云南省昆明市云南民族大学附属高级中学2023-2024学年高二上学期期中联考诊断性测试数学试题(已下线)模块六 立体几何 大招17 判二面角的锐钝问题
6 . 如图1,在三棱锥P-ABC中,PA⊥平面ABC,AC⊥BC,D为侧棱PC上一点,它的正(主)视图和侧(左)视图如图2所示.
![](https://img.xkw.com/dksih/QBM/2012/8/28/1570985983533056/1570985989070848/STEM/4fe8d96c50f3424c8a82fd6a56bdc77e.png)
(1) 证明:AD⊥平面PBC;
(2) 在∠ACB的平分线上确定一点Q,使得PQ∥平面ABD,并求此时PQ的长.
![](https://img.xkw.com/dksih/QBM/2012/8/28/1570985983533056/1570985989070848/STEM/4fe8d96c50f3424c8a82fd6a56bdc77e.png)
(1) 证明:AD⊥平面PBC;
(2) 在∠ACB的平分线上确定一点Q,使得PQ∥平面ABD,并求此时PQ的长.
您最近一年使用:0次
2013·广东韶关·一模
7 . 如图,长方体
中,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/17b118f7d08842de8760eab70ffafea3.png)
(1)求三棱锥
的体积;
(2)证明:
;
(3)求二面角
的正切值.
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/c22f0b58ffe5470ea706d123e0272507.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/626c7aca1d3346abbf7a9496eb082201.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/8fbf6d33e2c04ac4a2d45c3ad41921cf.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/01f8ce7444db463e81894180db143bbf.png)
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/17b118f7d08842de8760eab70ffafea3.png)
(1)求三棱锥
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/36a589513be945a9ba8516dcb231e552.png)
(2)证明:
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/e87cf8bd2b834ffea09730874247c0e1.png)
(3)求二面角
![](https://img.xkw.com/dksih/QBM/2013/10/21/1571369350823936/1571369356615680/STEM/7f7c097034cf470ab64b2a690a78fb40.png)
您最近一年使用:0次
8 . 如图(1),
是直径
的圆上一点,
为圆
的切线,
为切点,
为等边三角形,连接
交
于
,以
为折痕将
翻折到图(2)所示
的位置,点
为平面
外的点.
![](https://img.xkw.com/dksih/QBM/2011/5/23/1570217778290688/1570217783820288/STEM/857ee6a3118946339da7ae8739e29be4.png?resizew=330)
(1)求证:异面直线
和
互相垂直;
(2)若
为
上一点,且
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b280088a8f97b52c2145bc709434e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2011/5/23/1570217778290688/1570217783820288/STEM/857ee6a3118946339da7ae8739e29be4.png?resizew=330)
(1)求证:异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8459bfe1dd87957f217ffcd0d10f6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e89e99ab9c1ece0cc5c3bbabaa97de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3fc56bf641c7b18a562dc6c1c8290bc.png)
您最近一年使用:0次
12-13高二上·黑龙江大庆·开学考试
9 . 如图
,在三棱锥
中,
平面
,
,
为侧棱
上一点,它的正(主)视图和侧(左)视图如图
所示.
(
)证明:
平面
.
(
)求三棱锥
的体积.
(
)在
的平分线上确定一点
,使得
平面
,并求此时
的长.
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219848675328/1809934050557952/STEM/6ef207b0e144411795bfccdf8bb1b3d1.png?resizew=133)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e258c6995b058164df335e154692b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219848675328/1809934050557952/STEM/6ef207b0e144411795bfccdf8bb1b3d1.png?resizew=133)
![](https://img.xkw.com/dksih/QBM/2017/11/3/1809219848675328/1809934050557952/STEM/1041d663056042889cc4a4a01e46ed8a.png?resizew=234)
您最近一年使用:0次
2016-12-02更新
|
1497次组卷
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8卷引用:2012-2013学年广东省揭阳一中高一下学期第一次段考文科数学试卷
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2012·浙江台州·二模
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10 . 如图,AC是圆O的直径,点B在圆O上,∠BAC=30°,BM⊥AC交AC于点M,EA⊥平面ABC,FC//EA,AC=4,EA=3,FC=1.
(1)证明:EM⊥BF;
(2)求平面BEF与平面ABC所成的二面角的余弦值.
(1)证明:EM⊥BF;
(2)求平面BEF与平面ABC所成的二面角的余弦值.
![](https://img.xkw.com/dksih/QBM/2012/7/30/1570943890194432/1570943895568384/STEM/5e458b96-13c1-4413-af71-836dc330dd33.png?resizew=146)
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