名校
1 . 如图所示,在棱长为2的正方体
中,E,F,G分别为
,
,
的中点,则有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
A.直线![]() ![]() |
B.异面直线![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.平面![]() ![]() |
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解题方法
2 . 如图,在正方体
中,P为棱
上的动点,
平面
,Q为垂足,则( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c982eb645d77aa24c642fca6d72e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98fcaa21173e78d407bfa4170849e2eb.png)
A.![]() |
B.平面![]() |
C.当P位于![]() ![]() |
D.线段![]() ![]() |
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3 . 已知三棱锥
是边长为2的正三角形,
分别是
的中点,
在平面
内的投影为点
在平面
内的投影为点
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/899bb37ff0e8075cf8cf7d589be7d50d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a398d4645333a88e4a0816d5b7087702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b085fab4fc7b49bead663650b3bdeb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9521129014e5f138b49339d5b9f4dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526e2fe627bb4ddebe708c07d0a22fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() |
B.![]() ![]() ![]() |
C.![]() |
D.形如三棱锥![]() |
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450次组卷
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3卷引用:河南省郑州市2024届高三第三次质量预测数学试题
名校
解题方法
4 . 如图,
平面
,
,
,
,
,
为
中点.
∥平面
;
(2)求三棱锥
的体积;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88dac2c17c765517c2163ab43bbe1038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9906ec3e92ecdefb55d5b1d99a928e.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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解题方法
5 . 在正方体
中,M,N,P,Q分别是棱
,
,AB,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
A.PN与QM为异面直线 | B.![]() ![]() |
C.平面PMN截该正方体所得截面形状为等腰梯形 | D.点![]() ![]() |
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6 . 如图,在四棱锥
中,底面
是边长为1的正方形,
,
、
分别是
、
的中点.
平面
;
(2)若二面角
的大小为
,
(ⅰ)求
与
所成角的余弦值;
(ⅱ)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553dcd4a2d14d887ff40a307e81d1d3b.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/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95fd77c97244c7c5f84ca5e3fcc28e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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7 . 已知空间两条异面直线
所成的角等于60°,过点
与
所成的角均为
的直线有且只有一条,则
的值可以等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.30° | B.45° | C.75° | D.90° |
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8 . 如图,已知线段
为圆柱
的三条母线,
为底面圆
的一条直径,
是母线
的中点,且
.
平面DOC;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1921b3559a5f73426f0d78e401ecc75b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d9e45361c2504173963bb9687e1f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e5981445b6f2a6c58974158d96a4de.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eddaf3f33bd9a99162c061c9dd99aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
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名校
9 . 正多面体也称柏拉图立体(被誉为最有规律的立体结构),是所有面都只由一种正多边形构成的多面体(各面都是全等的正多边形).数学家已经证明世界上只存在五种柏拉图立体,即正四面体、正六面体、正八面体、正十二面体、正二十面体.已知一个正八面体
的棱长都是2(如图),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
A.![]() ![]() |
B.直线![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() |
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4卷引用:福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题
解题方法
10 . 在棱长为2的正方体
中,
分别是
,
,
的中点,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9369aed2d8309af46ac3eaffb9cce537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
A.![]() ![]() |
B.![]() ![]() |
C.多面体![]() |
D.平面![]() ![]() |
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4卷引用:江苏省南通市2023-2024学年高一下学期5月质量监测数学试题
江苏省南通市2023-2024学年高一下学期5月质量监测数学试题(已下线)6.5.1直线与平面垂直-【帮课堂】(北师大版2019必修第二册)福建省宁德市博雅培文学校2023-2024学年高一下学期5月月考数学试题陕西省西安市南开高级中学2023-2024学年高一下学期五月月考数学试卷