名校
1 . 如图,在四边形
中,
和
是全等三角形,
,
,
,
.下面有两种折叠方法将四边形
折成三棱锥.折法①;将
沿着
折起,得到三棱锥
,如图1.折法②:将
沿着
折起,得到三棱锥
,如图2.下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ebd86a076448d19401268f139b5b90.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/db4c18aba9681a8475968248764d4c3a.png)
A.按照折法①,三棱锥![]() ![]() |
B.按照折法①,存在![]() ![]() |
C.按照折法②﹐三棱锥![]() ![]() |
D.按照折法②,存在![]() ![]() ![]() ![]() ![]() ![]() |
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2卷引用:四川省遂宁市射洪中学校2023-2024学年高一下学期5月期中考试数学试题
名校
2 . 如图,在四棱锥
中,
,
,
,
,
.
时,求直线
与平面
所成角的大小;
(2)当二面角
为
时,求平面
与平面
所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6370d6c626bdabf1fc694501ee6c714f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1387a262fa090afe51656734c3422bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7ff7cf4d7094bc927e959157ef1b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)当二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351d71fa01d3f5920e374a8ee7b524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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7卷引用:四川省内江市第二中学2023-2024学年高二上学期12月月考数学试题
四川省内江市第二中学2023-2024学年高二上学期12月月考数学试题江苏省苏州市2022-2023学年高一下学期期末学业质量阳光指标调研数学试题(已下线)模块二 专题5《立体几何初步》单元检测篇 A基础卷 (苏教版)(已下线)第五篇 向量与几何 专题17 三正弦定理、三余弦定理 微点1 三正弦定理、三余弦定理上海市杨浦高级中学2023-2024学年高三上学期11月期中考试数学试卷(已下线)第二章 立体几何中的计算 专题一 空间角 微点11 三正弦定理与三余弦定理(一)【培优版】陕西省西安市铁一中学国际部2023-2024学年高一下学期第三月考数学试题
名校
3 . 如图,已知正方体
的棱长为1,
分别是棱
,
的中点.若点
为侧面正方形
内(含边界)的动点,且
平面
,则
与侧面
所成角的正切值最大为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa7d487586e3702f55cd2d6466654bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b668b5c01e0b1a529cc4e3efb2e9057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c413f509068d30b165f9d92bdba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/30/34c2d8e0-fbc5-4703-bbb8-d58ef3fbc657.png?resizew=160)
A.2 | B.1 | C.![]() | D.![]() |
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6卷引用:四川省成都市锦江区嘉祥外国语高级中学高2023届高三下学期三诊模拟考试数学(文科)试题
四川省成都市锦江区嘉祥外国语高级中学高2023届高三下学期三诊模拟考试数学(文科)试题(已下线)专题10 空间向量与立体几何-2(已下线)第03讲 直线、平面平行的判定与性质(练习)(已下线)第12讲 8.6.2直线与平面垂直的判定定理(第1课时)-【帮课堂】(人教A版2019必修第二册)(已下线)专题7.3 空间角与空间中的距离问题【九大题型】(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点6 角度的范围与最值问题(一)【基础版】
4 . 已知四棱锥
的底面ABCD是边长为2的菱形,且
,
,
,E为PB中点.
![](https://img.xkw.com/dksih/QBM/2023/6/27/3268837724741632/3269523867172864/STEM/f5a9942d32d1418ea60ad54777b58e08.png?resizew=217)
(1)证明:
;
(2)若PB与底面ABCD所成角的正弦值为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb96e0331eebe80ed1ff610faf531fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15eae3c2cb4274a947f6a011960934d.png)
![](https://img.xkw.com/dksih/QBM/2023/6/27/3268837724741632/3269523867172864/STEM/f5a9942d32d1418ea60ad54777b58e08.png?resizew=217)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)若PB与底面ABCD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502f49e759b623b5c3a8b901bb9882cc.png)
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5 . 在正方体
中,点
是线段
上一动点,则下列各选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/2b32d92c-e0f9-44e9-81c5-e6b1e5356f1a.png?resizew=173)
A.![]() |
B.![]() ![]() |
C. 三棱锥![]() |
D.直线![]() ![]() ![]() |
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2卷引用:四川省泸县第五中学2023-2024学年高二上学期开学考试数学试题
解题方法
6 . 如图,在四棱锥P—ABCD中,底面ABCD为矩形,侧棱
底面ABCD,
,
,
,E为PD的中点.
(2)在侧棱PAB内找一点N,使
面PAC,并求出N点到AB和AP的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
(2)在侧棱PAB内找一点N,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c7f7ffbb802aef097bbe1a9321691f.png)
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7 . 如图,在棱长为2的正方体
中,
,
,
,
,
均为所在棱的中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/26/5bd39d5b-13d2-4965-8fb0-8f3d167e89c8.png?resizew=160)
A.棱![]() ![]() ![]() |
B.设点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.过点![]() ![]() ![]() ![]() |
D.三棱锥![]() ![]() |
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2卷引用:四川省宜宾市第四中学校2023-2024学年高二上学期12月月考数学试题
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8 . 已知四棱锥P-ABCD中,PA⊥底面ABCD,
,AD=CD=1,∠BAD=120°,
,∠ACB=90°.
(1)求证:BC⊥平面PAC;
(2)求直线PC与平面PAB所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/20/244ed6eb-17d8-49af-8ce7-6c123f576b9e.png?resizew=160)
(1)求证:BC⊥平面PAC;
(2)求直线PC与平面PAB所成的角的正弦值.
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9 . 点
在以
为直径的球
的表面上,且
,
,已知球
的表面积是
,设直线
和
所成角的大小为
,直线
和平面
所成角的大小为
,四面体
内切球半径为
,下列说法中正确的个数是( )
①
平面
;②平面
平面
;③
;④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00b0d47c1f33748059cee20eb744156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02dba908a505cff93e0b297d00b82a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1716ac3f2868fcc4d86fad1c1c48c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00b0d47c1f33748059cee20eb744156.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:四川省成都市第七中学2024届高三零诊模拟考试数学(理)试题
名校
解题方法
10 . 已知直三棱柱
中,AB
BC,
,D是AC的中点,O为
的中点.点P是
上的动点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6ff6a807f5639faac835012b3728c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/19/c9155ac2-a702-474e-bdc7-e6eff2e098db.png?resizew=180)
A.点P在![]() ![]() |
B.当点P运动到![]() ![]() ![]() ![]() |
C.无论点P在![]() ![]() |
D.当点P运动到![]() ![]() ![]() ![]() |
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2卷引用:四川省宜宾市叙州区第一中学校2023-2024学年高二上学期开学考试数学试题