题型:
难度:
1 . 正八面体可由连接正方体每个面的中心构成,如图所示,在棱长为2的正八面体中,则有( )
![](/uploads/image/idqe2127/ebfdef2e-3c84-41ba-9d97-fafbee2b1f81.png)
a.直线![]() ![]() | b.平面![]() ![]() |
c.该几何体的体积为![]() | d.平面![]() ![]() ![]() |
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解答题-证明题
|
适中(0.65)
|
2 . 如图所示,在四棱锥
中,
平面,底面是正方形,且
,四棱锥
的体积为
.
![](/uploads/image/idqe2127/6af0b2c3-14da-4d9b-8fa8-f4373ab96384.png)
(1)求证:平面
平面
;
(2)求直线
与平面
所成的角;
(3)求点
到平面
的距离.
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](/uploads/image/squformula/fcd0ced286a0fbc7e4862f8147264277.png)
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/a391005600bdd69c96750589f9adb048.png)
![](/uploads/image/idqe2127/6af0b2c3-14da-4d9b-8fa8-f4373ab96384.png)
(1)求证:平面
![](/uploads/image/squformula/f04c222223dae9ef27d4c132534d9848.png)
![](/uploads/image/squformula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求直线
![](/uploads/image/squformula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](/uploads/image/squformula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)求点
![](/uploads/image/squformula/5963abe8f421bd99a2aaa94831a951e9.png)
![](/uploads/image/squformula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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37次组卷
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1卷引用:上海市上海财经大学附属中学2023-2024学年高二上学期期末考试数学试卷
单选题
|
较易(0.85)
|
解题方法
3 . 在某次数学探究活动中,小明先将一副三角板按照图1的方式进行拼接,然后他又将三角板
折起,使得二面角
为直二面角,得图2所示四面体.小明对四面体中的直线、平面的位置关系作出了如下的判断:①
平面
;②
平面
;③平面
平面
;④平面
平面
.其中判断正确的个数是( )
![](/uploads/image/idqe2123/19b81099-ab22-432e-a7e2-e118ace6c775.png)
![](/uploads/image/squformula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](/uploads/image/squformula/5ec2524be492bca0d1566bf848066f10.png)
![](/uploads/image/squformula/97f30533da2e1d2a958dc906c37eba9d.png)
![](/uploads/image/squformula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](/uploads/image/squformula/21f9157fce2a8339d281178c7c0bccbe.png)
![](/uploads/image/squformula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](/uploads/image/squformula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](/uploads/image/squformula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](/uploads/image/squformula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](/uploads/image/squformula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](/uploads/image/idqe2123/19b81099-ab22-432e-a7e2-e118ace6c775.png)
a.1 | b.2 |
c.3 | d.4 |
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解答题-证明题
|
适中(0.65)
|
名校
解题方法
4 . 如图,在四棱锥
中,
为等边三角形,
,
,且
,
,
,
为
中点.
(1)求证:平面
平面;
(2)若线段
上存在点
,使得二面角
的大小为,求
的值.
![](/uploads/image/squformula/0585b6c0f156eecf9662b9846d4eb693.png)
![](/uploads/image/squformula/55a675310c8ba418e5a59beb7317e21e.png)
![](/uploads/image/squformula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](/uploads/image/squformula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](/uploads/image/squformula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](/uploads/image/squformula/18120a244d3a1f9c1688bf53eb2ad775.png)
![](/uploads/image/squformula/ff0a0c299356c26338d4153748e8a61d.png)
![](/uploads/image/squformula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](/uploads/image/squformula/03902478df1a55bc99703210bccab910.png)
![](/uploads/image/idqe2110/f090b990-e56f-4d88-9053-950374bfddbe.png)
(1)求证:平面
![](/uploads/image/squformula/93edc7bb513f40a89173121c8570cd65.png)
(2)若线段
![](/uploads/image/squformula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](/uploads/image/squformula/acc290b44635265137fdf13146b6a6d9.png)
![](/uploads/image/squformula/5cbc8495936262640fe946e3974f40cf.png)
![](/uploads/image/squformula/c2942447b6af4f2749668439d5ee03a7.png)
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解答题-证明题
|
适中(0.65)
|
解题方法
5 . 如图,在多面体
中,底面为平行四边形,
平面
,
为等边三角形,
.
![](/uploads/image/idqe2125/6061f5b4-cfa2-4c40-8e61-18b59542251e.png)
(1)求证:平面
平面;
(2)求平面
与平面
夹角的余弦值.
![](/uploads/image/squformula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](/uploads/image/squformula/57f9d682e5d3cc8573574d8d11636758.png)
![](/uploads/image/squformula/b8e4e1cf88cd39a97137e84721894925.png)
![](/uploads/image/squformula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](/uploads/image/squformula/8461613963a3ca9c10a003574c4cb08b.png)
![](/uploads/image/idqe2125/6061f5b4-cfa2-4c40-8e61-18b59542251e.png)
(1)求证:平面
![](/uploads/image/squformula/bde1e200d1dd5ddc433c876c9d2f688c.png)
(2)求平面
![](/uploads/image/squformula/2977ae4bfa32de8c6f0fb136205c4fe7.png)
![](/uploads/image/squformula/7495688c046142f688c822209c0e968e.png)
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1卷引用:2024届河南省郑州市高三毕业班第一次质量预测(一模)数学试题
解题方法
6 . 已知空间中,l、m、n是互不相同直线,
、
是不重合的平面,则下列命题为真命题的是( )
![](/uploads/image/squformula/e170f206fdbbd834aad7580c727e2cc6.png)
![](/uploads/image/squformula/5b5858ee1ce52b251816757257a11c29.png)
a.若![]() ![]() ![]() ![]() |
b.若![]() ![]() ![]() |
c.若![]() ![]() ![]() ![]() ![]() |
d.若![]() ![]() ![]() |
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139次组卷
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1卷引用:上海市莘庄中学2023-2024学年高二上学期期末数学试题
名校
解题方法
7 . 如图所示,在棱长为2的正方体
中,
是线段
上的动点,则下列说法正确的是( )
![](/uploads/image/idqe2130/25df8722-2248-4b64-8eec-3dd9009fa9b6.png)
![](/uploads/image/squformula/6e09725691ee7851f54c0dee86b2bf55.png)
![](/uploads/image/squformula/dad2a36927223bd70f426ba06aea4b45.png)
![](/uploads/image/squformula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](/uploads/image/idqe2130/25df8722-2248-4b64-8eec-3dd9009fa9b6.png)
a.平面![]() |
b.![]() ![]() |
c.若直线![]() ![]() ![]() ![]() |
d.若![]() ![]() ![]() ![]() ![]() |
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927次组卷
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5卷引用:黑龙江省齐齐哈尔市2024届高三上学期期末数学试题
8 . 设
、
是两条不同的直线,
、
是两个不同的平面,则下列结论中正确的是( )
①若
,
,且
,则
; ②若
,
,且
,则
;
③若
,
,且
,则
; ④若
,
,且
,则
:
![](/uploads/image/squformula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](/uploads/image/squformula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](/uploads/image/squformula/e170f206fdbbd834aad7580c727e2cc6.png)
![](/uploads/image/squformula/5b5858ee1ce52b251816757257a11c29.png)
①若
![](/uploads/image/squformula/4042f9c51f83e3367d496e851735d7f9.png)
![](/uploads/image/squformula/5f4ded3c4bc7a2212f2a0eb5f9753de5.png)
![](/uploads/image/squformula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](/uploads/image/squformula/35f747152f006301e03b643afb80195c.png)
![](/uploads/image/squformula/4042f9c51f83e3367d496e851735d7f9.png)
![](/uploads/image/squformula/5f4ded3c4bc7a2212f2a0eb5f9753de5.png)
![](/uploads/image/squformula/84b6e422b2e6f6dada4d8c369559a077.png)
![](/uploads/image/squformula/a5986f2991d45fbf3578f08f27d9fd7e.png)
③若
![](/uploads/image/squformula/0fe920cd78db25f5b4df37d066e57800.png)
![](/uploads/image/squformula/a53cd751c44ad4d9ebd8e3243e751321.png)
![](/uploads/image/squformula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](/uploads/image/squformula/35f747152f006301e03b643afb80195c.png)
![](/uploads/image/squformula/0fe920cd78db25f5b4df37d066e57800.png)
![](/uploads/image/squformula/a53cd751c44ad4d9ebd8e3243e751321.png)
![](/uploads/image/squformula/84b6e422b2e6f6dada4d8c369559a077.png)
![](/uploads/image/squformula/a5986f2991d45fbf3578f08f27d9fd7e.png)
a.①②③ | b.①③④ | c.②④ | d.③④ |
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1卷引用:内蒙古自治区赤峰市2020-2021学年高一下学期期末联考文科数学试题(a)
解答题-证明题
|
适中(0.65)
|
名校
解题方法
9 . 已知平行四边形如图甲,
,
,沿
将
折起,使点
到达点
位置,且
,连接
得三棱锥
,如图乙.
![](/uploads/image/idqe2125/6b7d9da4-61fd-4f1e-bc6e-7e78903cfb91.png)
(1)证明:平面
平面
;
(2)在线段
上是否存在点
,使二面角
的余弦值为
,若存在,求出
的值,若不存在,请说明理由.
![](/uploads/image/squformula/efd0e8f705192e7012805abde99adb2e.png)
![](/uploads/image/squformula/2adde96c75990ec0a5d25f7057b77d56.png)
![](/uploads/image/squformula/60ef95894ceebaf236170e8832dcf7e3.png)
![](/uploads/image/squformula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](/uploads/image/squformula/8455657dde27aabe6adb7b188e031c11.png)
![](/uploads/image/squformula/dad2a36927223bd70f426ba06aea4b45.png)
![](/uploads/image/squformula/307d38cc7012c328f1f22aa793fe76d7.png)
![](/uploads/image/squformula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](/uploads/image/squformula/63397cda22cb1fad59cf966dfb588643.png)
![](/uploads/image/idqe2125/6b7d9da4-61fd-4f1e-bc6e-7e78903cfb91.png)
(1)证明:平面
![](/uploads/image/squformula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](/uploads/image/squformula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)在线段
![](/uploads/image/squformula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](/uploads/image/squformula/ac047e91852b91af639feec23a9598b2.png)
![](/uploads/image/squformula/a2e9ac46aabe38e5ea1a8cb0febc98af.png)
![](/uploads/image/squformula/d5ec70bc9d4f8f5df312e2f09ee3bcb5.png)
![](/uploads/image/squformula/bd088fbf960bc8d04067b6128c8cba20.png)
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解答题-证明题
|
适中(0.65)
|
名校
10 . 如图,在四棱锥
中,
,
,
,
,
,
,
.
![](/uploads/image/idqe212/e199e817-cc37-479a-afd1-bb132cd9b7d4.png)
(1)求证:平面
平面;
(2)若
为
上一点,且
,求直线
与平面所成角的正弦值.
![](/uploads/image/squformula/80c753cb1eb73fd8d136d00462970797.png)
![](/uploads/image/squformula/5f79863ffcfa63117ca6741b20a48e69.png)
![](/uploads/image/squformula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](/uploads/image/squformula/1aa6481beb14c81b1371fdcede025b5e.png)
![](/uploads/image/squformula/b98d3a8a7488e6a47fe18242e92316c5.png)
![](/uploads/image/squformula/62c9a6255f54f395572a922c801aa490.png)
![](/uploads/image/squformula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](/uploads/image/squformula/75929268210da5976bc37d080da030dd.png)
![](/uploads/image/idqe212/e199e817-cc37-479a-afd1-bb132cd9b7d4.png)
(1)求证:平面
![](/uploads/image/squformula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
(2)若
![](/uploads/image/squformula/ac047e91852b91af639feec23a9598b2.png)
![](/uploads/image/squformula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](/uploads/image/squformula/6c457163e0c9ac56a78400b5a713ae4c.png)
![](/uploads/image/squformula/15a424b50eaeafa6f302ffd95476cb86.png)
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