1 . 如图,正方形
的边长为1,正方形
所在平面与平面
互相垂直,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/40a599c4-e52f-44e3-bef3-3607dd994c7d.png)
(1)求证:
平面
;
(2)求证:
;
(3)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/cd4593287214468b9f5343d3148070c5.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/870bff5fc0584b4ea927c9c25db8d8a1.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/cd4593287214468b9f5343d3148070c5.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/bac69173fe9b402c8e6f3db24d2007ea.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/7e437572ab474dc8b91ab683b65adcc4.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/40a599c4-e52f-44e3-bef3-3607dd994c7d.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/4e37268c2f884d7f86ba1510c3ef3a7d.png)
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/a1ac04b2cf04497caf3c34b08f69eacb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc4c50ada59b5838d296697a8e0bb8d.png)
(3)求三棱锥
![](https://img.xkw.com/dksih/QBM/2015/8/7/1572205183311872/1572205189005312/STEM/fcfaed65b36041d9bd03ff656a6b3760.png)
您最近一年使用:0次
2 . 如图,四边形
是正方形,△
与△
均是以
为直角顶点的等腰直角三角形,点
是
的中点,点
是边
上的任意一点.
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572027454300160/1572027459665920/STEM/11089b4bf19946629b08c59efbc2ec56.png)
(1)求证:
;
(2)求二面角
的平面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572027454300160/1572027459665920/STEM/11089b4bf19946629b08c59efbc2ec56.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ddaefd87840c63bb301477bfabf5b26.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea71ca581022f0091a634db730ac77ba.png)
您最近一年使用:0次
2016-12-03更新
|
3708次组卷
|
6卷引用:2015届广东省广州市高三1月模拟理科数学试卷
2015届广东省广州市高三1月模拟理科数学试卷2015-2016学年河南省信阳高中高二12月考理科数学试卷人教A版高中数学必修二 2.3.2 平面与平面垂直的判定安徽省阜阳市太和第一中学2020-2021学年高二(平行班)上学期开学考试数学试题(已下线)第六章 立体几何初步(基础过关)-2020-2021学年高一数学单元测试定心卷(北师大2019版必修第二册)湖南省长沙市雅礼中学2020-2021学年高二上学期期末数学试题
14-15高二上·广东汕头·期末
名校
3 . 如图,
为圆
的直径,点
.
在圆
上,且
,矩形
所在的平面和圆
所在的平面互相垂直,且
,
.
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585936973824/STEM/e70bdd0a74af4b1dad1f9bf296ec83af.png)
(1)设
的中点为
,求证:
平面
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c91baecb97fadd4f8ab49e6effcbc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a951292add4574c1debd16800674e1e.png)
![](https://img.xkw.com/dksih/QBM/2014/3/28/1571585931689984/1571585936973824/STEM/e70bdd0a74af4b1dad1f9bf296ec83af.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280247d7df395bb9ea78c51e67b458d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c93a34cbd4c0dc198b74524c0e05a10.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e7b3a2c6ad3c82b8091e721c58e4e2.png)
您最近一年使用:0次
4 . 如图,四棱锥
中,底面
为平行四边形,
底面
,
是棱
的中点,
且
.
![](https://img.xkw.com/dksih/QBM/2017/9/2/1765395891019776/1766284314329088/STEM/8d6d454cd5a04b7cb0322403aa363d9e.png?resizew=220)
(1)求证:
平面
;
(2)如果
是棱
上一点,且直线
与平面
所成角的正弦值为
,求
的值.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890c5b938c7a39a891faeaac4d77aee8.png)
![](https://img.xkw.com/dksih/QBM/2017/9/2/1765395891019776/1766284314329088/STEM/8d6d454cd5a04b7cb0322403aa363d9e.png?resizew=220)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d109733379365295b93c58769d2019.png)
您最近一年使用:0次
2016-12-13更新
|
1590次组卷
|
4卷引用:【校级联考】广东省汕头市达濠华侨中学,东厦中学2019届高三上学期第三次联考数学(理)试题
5 . 如图,在四棱锥
中,
平面
,底面
是菱形,
,
为
与
的交点,
为
上任意一点.
(1)证明:平面
平面
;
(2)若
平面
,并且二面角
的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86db010859f7a243badec02946a4e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36222db36e348661eb5f616820e4e60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ccfd81d120348601cd611241d1a5dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af53bde2b93b4707c79d00010ac9ff06.png)
![](https://img.xkw.com/dksih/QBM/2018/3/25/1909534314594304/1912476343926784/STEM/d7f94517aeb34b6b99a53db8b1b90065.png?resizew=164)
您最近一年使用:0次
2016-12-03更新
|
17次组卷
|
4卷引用:2015届广东省汕头市潮南区高三高考模拟二理科数学试卷
6 . 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
7 . 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
8 . 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
9 . 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
10 . 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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