名校
解题方法
1 . 正三棱柱
中,
为棱
的中点,
为线段
(不包括端点)上一动点,
分别为棱
上靠近点
的三等分点,过
作三棱柱
的截面
,使得
垂直于
且交
于点
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31dea35a4e0ca65105e1f12aeb0fe5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() ![]() | B.存在点![]() ![]() ![]() |
C.当![]() ![]() ![]() | D.三棱锥![]() ![]() |
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2024-06-17更新
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359次组卷
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3卷引用:安徽省县中联盟(江南十校)2023-2024学年高一下学期5月月考数学试题
安徽省县中联盟(江南十校)2023-2024学年高一下学期5月月考数学试题河南省安阳市林州市第一中学2023-2024学年高一下学期5月月考数学试题(已下线)专题07 立体几何小题常考题型归类-期末考点大串讲(人教B版2019必修第四册)
名校
2 . 如下左图,矩形
中,
,
,
.过顶点
作对角线
的垂线,交对角线
于点
,交边
于点
,现将
沿
翻折,形成四面体
,如下右图.
外接球的体积;
(2)求证:平面
平面
;
(3)若点
为棱
的中点,请判断在将
沿
翻折过程中,直线
能否平行于面
.若能请求出此时的二面角
的大小;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864c21e9664fa9111ede6425b09563a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864c21e9664fa9111ede6425b09563a.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adaed034e575b208bdb8dca7bad66957.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adaed034e575b208bdb8dca7bad66957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
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2024-06-12更新
|
472次组卷
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2卷引用:安徽省级示范高中培优联盟2023-2024学年高一下学期春季联赛数学试题
名校
解题方法
3 . 如图,将边长为2的正六边形
沿对角线
折起,记二面角
的大小为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
,连接
,
构成多面体
.
平面
;
(2)问当
为何值时,直线
到平面
的距离等于
?
(3)在(2)的条件下,求多面体
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6238a6fb52a9d2e3521ba66ef9a5c247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8560ca9023cf64637ce1467f338556bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9eb9126c7053574c62b897582ad49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94270844f197d524bf1da4f1385befd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
(2)问当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(3)在(2)的条件下,求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fca9eb9126c7053574c62b897582ad49.png)
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2024-06-08更新
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176次组卷
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2卷引用:安徽省金榜教育2023-2024学年高一下学期5月阶段性大联考数学试题
名校
解题方法
4 . 已知m,n是异面直线,
,
,那么( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/539a38ada26356d73024fb8533449c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209323a7a4d015f7e570ec578c1731f7.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-26更新
|
2806次组卷
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2卷引用:安徽省六安市六安第一中学2024届高考模拟预测数学试题(四)
名校
解题方法
5 . 在正三棱台
中,
,
,
,
,
,过MN与
平行的平面记为
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54638dd4ebf19815a1333d84e42f927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fa561a0bbdcabe625904937d40ca4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c97b0eaa963452e5e2bbd886daf60b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.四面体![]() ![]() | B.四面体![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2023-05-24更新
|
831次组卷
|
3卷引用:安徽省临泉第一中学2023届高三下学期模拟考试(三模)数学试题
名校
解题方法
6 . 在正三棱锥
中,
分别为棱
的中点,
分别在线段
上,且满足
,则下列说法一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75dc5b9679ae83920b94dbdfd14b0648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d3a6a3c54c77999e7804169c72f617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c8e6d76f3b649d52032999209b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3915237d7256f139add25576584cc6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcaf87ad4f498be78880f2bd5db0221f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9535b2f577103e9fb7fb28e01ba1520.png)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.直线![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2023-05-07更新
|
608次组卷
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3卷引用:安徽省马鞍山市2023届高三三模数学试题
安徽省马鞍山市2023届高三三模数学试题河北省唐山市曹妃甸区第一中学2022-2023学年高一下学期期末数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点1 异面直线所成角(一)【培优版】
名校
7 . 如图,在圆台
中,
分别为上、下底面直径,且
,
,
为异于
的一条母线.
为
的中点,证明:
平面
;
(2)若
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/601050d23e9d0b81ee6c5eda991dbdf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86605a29fe8fff454e0db6b86047a8fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439cf259dd6137aa31bb99244a04ddfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afabf56cc68ea438a890f9fea04b708e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc9e0457471047bc750ecd31989414a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6647d7d03d64dc6eac2c9651badd9376.png)
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2023-03-29更新
|
5596次组卷
|
14卷引用:2024届安徽省阜阳市皖江名校联盟高三模拟预测数学试题
2024届安徽省阜阳市皖江名校联盟高三模拟预测数学试题江苏省八市(南通、泰州、扬州、徐州、淮安、连云港、宿迁、盐城)2023届高三二模数学试题重庆市缙云教育联盟2023届高三二模数学试题(已下线)专题07立体几何的向量方法(已下线)押新高考第20题 立体几何(已下线)江苏省八市2023届高三二模数学试题变式题17-22专题16空间向量与立体几何(解答题)江苏省部分四星级高中2023-2024学年高三上学期期初调研数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期期初调研数学试题广东省湛江市第一中学2023-2024学年高二上学期第一次大考数学试题江苏省八市2023届高三下学期第二次调研测试数学试题江苏省镇江市扬中市第二高级中学2023-2024学年高三上学期期末模拟数学试题3(已下线)空间向量与立体几何江苏省南京外国语学校2023-2024学年高三上学期期中模拟数学试题
名校
解题方法
8 . 在三棱锥
中,
,
,
,
分别是
,
,
,
的重心.则下列命题中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() ![]() | B.![]() |
C.四条直线![]() ![]() ![]() ![]() | D.![]() |
您最近一年使用:0次
2023-03-25更新
|
837次组卷
|
2卷引用:安徽省安庆市2023届高三模拟考试(二模)数学试题
名校
9 . 如图,圆台
的轴截面为等腰梯形
,
,B为底面圆周上异于A,C的点.
内,过
作一条直线与平面
平行,并说明理由;
(2)设平面
∩平面
,
与平面QAC所成角为
,当四棱锥
的体积最大时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c6d80251fdeabfebd65bca460d55b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f664c0db517bec6886ff0b6100fd474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bd886276f8ff9df2a42013b337d726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a0c82028e1259f300facd32775a15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c6c1f6d821af7e3c8058993218a861.png)
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2023-02-25更新
|
2345次组卷
|
8卷引用:安徽省合肥一六八中学等学校2024届高三上学期名校期末联合测试数学试题
名校
解题方法
10 . 如图,P为平行四边形ABCD所在平面外一点,过BC的平面与平面PAD交于EF,E在线段PD上且异于P、D,则四边形EFBC是( )
A.空间四边形 | B.矩形 | C.梯形 | D.平行四边形 |
您最近一年使用:0次
2022-05-08更新
|
1347次组卷
|
7卷引用:2023年2月安徽省普通高中学业水平考试数学模拟试题(三)
2023年2月安徽省普通高中学业水平考试数学模拟试题(三)天津市南开中学2021-2022学年高一下学期期中数学试题(已下线)专题22 空间中的平行关系(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)8.5.2 直线与平面平行(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)4.3.2 直线与平面平行的性质(已下线)8.5空间直线、平面的平行——课后作业(巩固版)陕西省西安市西安中学2023-2024学年高二学考仿真考试数学试题