1 . 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
2 . 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)
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12-13高二上·黑龙江大庆·开学考试
3 . 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)
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2016-12-02更新
|
1497次组卷
|
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
(已下线)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(已下线)2012-2013学年黑龙江大庆实验中学高二上学期开学考试文科数学试卷(已下线)2012-2013学年湖北武汉部分重点中学高二上学期期末考试文科数学卷北京市海淀清华附永丰学校2016-2017学年高二上学期期中考试数学试题(已下线)专题46 空间向量与立体几何大题解题模板-2021年高考一轮数学单元复习一遍过(新高考地区专用)(已下线)专题46 空间向量与立体几何大题解题模板-2021年高考一轮数学(理)单元复习一遍过(已下线)专题43 立体几何大题解题模板-2021年高考一轮数学(文)单元复习一遍过(已下线)专题03 立体几何大题解题模板-(新教材)2020-2021学年高二数学单元复习(人教A版选择性必修第一册)
2012·浙江台州·二模
名校
4 . 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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2016-12-01更新
|
1376次组卷
|
9卷引用:广东省广州市第二中学高二上学期数学人教A版选修2-1模块测试试卷
广东省广州市第二中学高二上学期数学人教A版选修2-1模块测试试卷(已下线)2012届浙江省台州中学高三下学期第二次统练文科数学(已下线)2012届浙江省宁波市五校高三适应性考试理科数学试卷(已下线)2012届浙江省东阳中学高三5月模拟考试理科数学试卷(已下线)2014届浙江省绍兴市第一中学高三上学期回头考试理科数学试卷2016届海南省文昌中学高三上学期期末考试理科数学试卷2017届陕西师范大学附属中学高三上学期第二次模考数学(理)试卷陕西省西安市长安区第一中学2017届高三4月模拟考试数学(理)试题2018届高三数学训练题:阶段滚动检测试题(六)
5 . 如图,在四棱锥
中,
为等边三角形,平面
平面
,四边形
是高为
的等腰梯形,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/8/17/1572981128044544/1572981262655488/STEM/4c8e3526fde04c8ea0d630b3dcc77246.png)
(1)求证:
;
(2)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38b4f2a97f7ed95473d864f5c2accf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425e79e4e7c13e2ea8ae3d4f8d31ac33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d2956faa9fea992d3b68e10bd8bfea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa049fadd0ce35fa7ae25e02112afef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03952d664fba91020fc5f3bcf2f9746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e501b69b1da5d5fc0a30581088af0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2016/8/17/1572981128044544/1572981262655488/STEM/4c8e3526fde04c8ea0d630b3dcc77246.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8f4790cfa8693b4901edb1a49c4d2c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2016-12-04更新
|
440次组卷
|
3卷引用:2015-2016学年广东省惠州一中高二4月月考文科数学试卷
6 . 如图,四棱锥
,侧面
是边长为
的正三角形,且与底面垂直,底面
是
的菱形,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572961266122752/1572961272643584/STEM/6aebd8b00d164319bf6a1535a43408cc.png)
(Ⅰ)求证:
;
(Ⅱ)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fbe4053a65b67949981f24c0d30b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf5cb457a768676c10da10ccfdbb2fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b0c4c783dd55685bd3e88bb31c6696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba122ff4fb6c7f5a107b3ec970ad43b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9c827e46d1a395fafbf15cdd6c6c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435f34602291e9e293ff64a1606e29dc.png)
![](https://img.xkw.com/dksih/QBM/2016/8/4/1572961266122752/1572961272643584/STEM/6aebd8b00d164319bf6a1535a43408cc.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac0e1293aae6c92e1d5d255cb16077f.png)
(Ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0b669ef4514f24ee09adeff7f41238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9127c2f1a2ad85020d558953f2c2199a.png)
您最近一年使用:0次
7 . 如图,AB是圆O的直径,C是圆O上除A、B外的一点,DC⊥平面ABC,四边形CBED为矩形,CD=1,AB=4.
![](https://img.xkw.com/dksih/QBM/2016/7/8/1572896713433088/1572896719560704/STEM/9c233e64fbbf43ceb4f69ce5672ecb87.png)
(1)求证:ED⊥平面ACD;
(2)当三棱锥E﹣ADC体积取最大值时,求此刻点C到平面ADE的距离.
![](https://img.xkw.com/dksih/QBM/2016/7/8/1572896713433088/1572896719560704/STEM/9c233e64fbbf43ceb4f69ce5672ecb87.png)
(1)求证:ED⊥平面ACD;
(2)当三棱锥E﹣ADC体积取最大值时,求此刻点C到平面ADE的距离.
您最近一年使用:0次
2016-12-04更新
|
414次组卷
|
2卷引用:2015-2016学年广东省汕头金山中学高二上期末文科数学试卷
8 . 如图所示,四棱锥
中,底面
为矩形,
,
,点
为
的中点.
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/c77539d8ec3f41e292777957159fc18f.png)
(1)求证:
;
(2)求证:
.
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/1fa21c4d850e44668f8d9cc6028acddf.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/20d7b9726bf345d2b52d64086c2e722f.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/c1fd1e9e8c5f4d369004f694c52a9906.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/c5d64f7869ed4d7e83f8640a8a764f4a.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/a16ca307e1f445b7a01ac8b7c703a723.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/39e563df67cd47a9b754d019e044499f.png)
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/c77539d8ec3f41e292777957159fc18f.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/a4d9b498470a4ed1a7463ba916a4bff9.png)
(2)求证:
![](https://img.xkw.com/dksih/QBM/2016/5/11/1572632161345536/1572632167522304/STEM/8598ecf4d0a943baa59265b89f856f79.png)
您最近一年使用:0次
9 . 如图所示,在三棱柱
中,
为正方形,
为菱形,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2016/4/29/1572611780354048/1572611786670080/STEM/0cf0e473d2494cafbcb2a6b2bc5a0fd5.png?resizew=200)
(Ⅰ)求证:
;
(Ⅱ)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b51221630159e52bda685680fa684d8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce04b35c265cc9c48b60204bd2f718ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://img.xkw.com/dksih/QBM/2016/4/29/1572611780354048/1572611786670080/STEM/0cf0e473d2494cafbcb2a6b2bc5a0fd5.png?resizew=200)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb81a917e1183890a82885b350b63f14.png)
(Ⅱ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dfb64c679bf4a62e5ee092d8885fc09.png)
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10 . 如图,在直三棱柱
中,平面
侧面
,且
.
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772605952/STEM/9b83dc6e25ee48d7975690c9b755fc49.png)
(1)求证:
;
(2)若
,求锐二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d7e638ee7e910e4dd7fec67b9b75da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://img.xkw.com/dksih/QBM/2016/3/1/1572508766109696/1572508772605952/STEM/9b83dc6e25ee48d7975690c9b755fc49.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af254745c1c19bd20e83344bee674ce7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c127b47353581fe4626d55345a5cb4eb.png)
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