1 . 如图,正四棱锥
的底面是边长为
的正方形,侧棱长是底面边长为
倍,
为底面对角线的交点,
为侧棱
上的点.
![](https://img.xkw.com/dksih/QBM/2015/8/25/1572220230975488/1572220236660736/STEM/7d70172218c543c58c58ac6a6b031c7d.png)
(1)求证:
;
(2)
为
的中点,若
平面
,求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aa0d36da718de7c50a781b8e2bb8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://img.xkw.com/dksih/QBM/2015/8/25/1572220230975488/1572220236660736/STEM/7d70172218c543c58c58ac6a6b031c7d.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d785b183d9b7ddf4f9f60ca49a2fc3ba.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab3cc5d6891b01c98e1429da8a58d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2 . 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
3 . 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
4 . 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
5 . 如图,四棱锥P﹣ABCD中,底面四边形ABCD是正方形,PA=AB=1,PA⊥平面ABCD,E为棱PB上一点,PD∥平面ACE,过E作PC的垂线,垂足为F.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572592954769408/1572592960905216/STEM/9c8d38337abe4edea3fc175a52b5d3a4.png)
(Ⅰ)求证:PC⊥平面AEF;
(Ⅱ)求三棱锥P﹣AEF的体积.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572592954769408/1572592960905216/STEM/9c8d38337abe4edea3fc175a52b5d3a4.png)
(Ⅰ)求证:PC⊥平面AEF;
(Ⅱ)求三棱锥P﹣AEF的体积.
您最近一年使用:0次
6 . 如图所示,在直三棱柱
中,
,
,
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/a360770cad0049318dc29dfdcee604cd.png)
(Ⅰ)求证:
;
(Ⅱ)求证:
.
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/fbef4db8d5aa423cbacb95006f89ae1e.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/50ecfc2a16a04fabba73e5b1af347b32.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/e7623c64bc4b41159bfe1cdfffdafbaf.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/5e052a2152af4d8bbecfe31c6b2aec84.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/ece7110146a040c6a825b421209f8244.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/bdf323d2e36649dabaf6e39394969b03.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/5627290e743141d89541ec5af569e78b.png)
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/a360770cad0049318dc29dfdcee604cd.png)
(Ⅰ)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/a44ac4711047478eae32b5ade1ca7f06.png)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2015/8/6/1572200275312640/1572200281006080/STEM/ffb18a06fe65498f9409b0a42500bab6.png)
您最近一年使用:0次
7 . 长方体
中,
,
,点
为
中点.
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497781760/STEM/d9abb2855702425a8a8f1d28fd447987.png)
(Ⅰ)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
平面
;
(Ⅱ)求证:
平面
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8456cee87c4e22351affc28f3a73a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a53ecb573efb44465fa11b22f9198e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/7/10/1572178491924480/1572178497781760/STEM/d9abb2855702425a8a8f1d28fd447987.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb8b9b4d0fded993bf8b618f0820407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
您最近一年使用:0次
8 . 如图,已知PA⊥⊙O所在的平面, AB是⊙O的直径,AB=2,C是⊙O上一点,且AC=BC=PA,E是PC的中点,F是PB的中点.
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572032055377920/1572032061259776/STEM/63436f5ac9e34b538fc2655e68edce4c.png)
(1)求证:EF//平面ABC;
(2)求证:EF⊥平面PAC;
(3)求三棱锥B—PAC的体积.
![](https://img.xkw.com/dksih/QBM/2015/3/25/1572032055377920/1572032061259776/STEM/63436f5ac9e34b538fc2655e68edce4c.png)
(1)求证:EF//平面ABC;
(2)求证:EF⊥平面PAC;
(3)求三棱锥B—PAC的体积.
您最近一年使用:0次
2016-12-03更新
|
1015次组卷
|
2卷引用:2015届广东省肇庆市高中毕业班第一次统一检测文科数学试卷
9 . 如图,在五面体
中,四边形
是边长为
的正方形,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571679744958464/1571679750889472/STEM/2aefb6579d1e4894823827e914002c6f.png)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07b92b8282c7fd1158b3b5098e38c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d1b2f8e921264ebe993d8e36587e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6166b9a5437671bcba31e17c375eb39.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571679744958464/1571679750889472/STEM/2aefb6579d1e4894823827e914002c6f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbe3ec31a79a171dcf274ff99e50762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2016-12-02更新
|
1757次组卷
|
3卷引用:2014届广东省广州市普通高中毕业班综合测试二理科数学试卷
10 . 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