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1 . 给出以下四个命题:
①斜棱柱的侧面展开图一定是一个平行四边形;
②若直线
与直线
异面,且
平面
,则
与
的位置关系是平行或相交;
③如果两条平行线中有一条平行于这个平面,那么另外一条直线也平行于该平面;
④若正方体的截面形状是四边形,则该四边形必有一组边平行.
其中正确的命题是______ .(填写序号).
①斜棱柱的侧面展开图一定是一个平行四边形;
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaf5492ffc6db02fd5968b643c8b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
③如果两条平行线中有一条平行于这个平面,那么另外一条直线也平行于该平面;
④若正方体的截面形状是四边形,则该四边形必有一组边平行.
其中正确的命题是
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2 . 已知正方体
的各顶点均在表面积为
的球面上,
为该球面上一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02dba908a505cff93e0b297d00b82a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.存在无数个点![]() ![]() ![]() ![]() |
B.当平面![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() ![]() |
D.存在无数个点![]() ![]() ![]() |
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2023-09-01更新
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3卷引用:广东省广州市空港实验中学2024届高三上学期期中数学试题
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3 . 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
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14卷引用: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
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2024届安徽省阜阳市皖江名校联盟高三模拟预测数学试题
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解题方法
4 . 如图,线段
是圆柱
的母线,
是圆柱下底面
的内接正三角形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/8258e722-559c-4234-adbe-98aaf43fd125.png?resizew=140)
(1)劣弧
上是否存在点D,使得
平面
?若存在,求出劣弧
的长度;若不存在,请说明理由.
(2)求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effe791cf7422d81981f7f188e30dd76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/8258e722-559c-4234-adbe-98aaf43fd125.png?resizew=140)
(1)劣弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5483adc72a04c578f3b33b010720194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76528e1056b52c4023421fba749aabed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982a72de174de5de98aa58b4c7d5a886.png)
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2022-11-11更新
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6卷引用:湖北省部分重点高中2022-2023学年高二下学期4月联考数学试题
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5 . 如图,在五面体
中,底面
为矩形,
和
均为等边三角形,
平面
,
,
,且二面角
和
的大小均为
.设五面体
的各个顶点均位于球
的表面上,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/9922bed7-bbff-4246-a837-64a6972fd2e9.png?resizew=215)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a04a2b317c5a6b8b7eb5d760fbd818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e2bf04b646d77e272034198d21a1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5219d5b2c63eded763670e5800dd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ba310682e25a0c6d488e6aff816614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5292af357a9c81f104ff2237053a4d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c2044ecc165365634e21f3e95ec7f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8b7a29b332ac3a192a2c19efa1f886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadd8e8730b81d153ffa6c55a3ac68e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a04a2b317c5a6b8b7eb5d760fbd818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/9922bed7-bbff-4246-a837-64a6972fd2e9.png?resizew=215)
A.有且仅有一个![]() ![]() |
B.有且仅有两个![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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6卷引用:浙江省杭州学军中学2022-2023学年高二上学期期中模拟数学试题
浙江省杭州学军中学2022-2023学年高二上学期期中模拟数学试题湖北省云学新高考联盟学校2022-2023学年高二上学期10月联考数学试题2023年普通高等学校招生星云线上统一模拟考试Ⅰ数学试卷(已下线)模拟卷02(已下线)专题06 一网打尽外接球与内切球问题(精讲精练)-3广东省广州七中2023届高三上学期1月月考数学试题
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6 . 已知底面边长和斜高长均为2的正四棱锥被平行于底面的平面所截得的正棱台为
,且满足
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9dcbb4a05aa3b0cf780baa4489556e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)求棱台的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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7 . 如图1,在矩形
与菱形
中,
,
,
,
分别是
,
的中点.现沿
将菱形
折起,连接
,
,构成三棱柱
,如图2所示,若
,记平面
平面
,则( )
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/66b7b4d75a89494d80b15fba956f4073.png?resizew=158)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/c3c21240789448b48b396eb70adfd673.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0041488020a3e19377b18a70fbf82e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c89f9fb5d1a84be8aee78dca23090d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5089d811caeed93dc3bcc108d122a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5214ffa82aa775edc14bf625edd54cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee618381a1176c3f1504cc059eb2010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23205fa9081ee5fe649093380d61640.png)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/66b7b4d75a89494d80b15fba956f4073.png?resizew=158)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844657931567104/2844713479184384/STEM/c3c21240789448b48b396eb70adfd673.png?resizew=158)
A.平面![]() ![]() | B.![]() |
C.直线![]() ![]() | D.四面体![]() ![]() |
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2021-11-05更新
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5卷引用:山东省青岛市青岛第五十八中学2021-2022学年高三上学期期中数学试题
山东省青岛市青岛第五十八中学2021-2022学年高三上学期期中数学试题山东省青岛市青岛第十九中学2021-2022学年高三上学期期中数学试题2022年全国著名重点中学领航高考冲刺试卷(一)数学试题(已下线)考点33 直线与平面所成的角【理】-备战2022年高考数学典型试题解读与变式(已下线)热点06 空间位置关系的判断与证明-2022年高考数学【热点·重点·难点】专练(全国通用)
8 . 下列关于直线与平面间的位置关系的命题判断正确的是( ).
A.若空间中四条直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
B.设![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.直线![]() ![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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9 . 如图,作出平面EFG截长方体所得的截面(不必写出画图步骤,但需保留作图痕迹).
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