1 . 如图,在四面体
中,
,
,
为
的中点,
为
上一点.
平面BDF;
(2)若
,
,
.
(ⅰ)求二面角
的余弦值;
(ⅱ)求直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8726e6a11ad400cfd860b09debe475be.png)
(ⅰ)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
(ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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2 . 如图,已知正方体
的棱长为
.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4645450a006f2c20087486d0833afbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239198e40085b7dcffbe747c9c265a05.png)
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3 . 如图,在正方形
中,E,F分别是BC,CD的中点,现在沿AE,AF及EF把这个正方形折成一个空间图形,使B,C,D三点重合,重合后的点记为G,且取EF中点为O,则在这个空间图形中必有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 如图,AB是⊙O的直径,PA垂直于⊙O所在的平面,C是圆周上不同于A,B的一动点.
是直角三角形;
(2)若
,
,求直线AB与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71807a35b3170fce28ee6edf4c00d083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-06-17更新
|
803次组卷
|
2卷引用:吉林省长春市第二实验中学2023-2024学年高一下学期期中考试数学试题
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5 . 如图,在四棱锥
中,底面
是正方形,
平面
,且
,点
为线段
的中点.
平面
;
(2)求证:
平面
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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6 . 四棱台
中,
底面
,
是直线
上的两个动点,两个底面是正方形,
,
,
,
,则下列叙述正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.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/4901a7eda97d6a307db76c4fb196ba3d.png)
A.侧棱![]() ![]() |
B.侧面![]() |
C.该棱台的全面积是![]() |
D.三棱锥![]() |
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7 . 刻画空间的弯曲性是几何研究的重要内容,用曲率刻画空间的弯曲性,规定:多面体顶点的曲率等于2π与多面体在该点的面角之和的差,其中多面体的面的内角叫做多面体的面角,角度用弧度制.例如:正四面体每个顶点均有3个面角,每个面角均为
,故其各个顶点的曲率均为
.如图,在直三棱柱
中,点A的曲率为
,N,M分别为AB,
的中点,且
.
平面
.
(2)证明:平面
平面
.
(3)若
,求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7b2dd83fcacead6b6c7733503dfcee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e79fd1a2ba4245c902b45bf9fc5c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00c25c4259d935d6e6fabe5c3fc1f43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0b52ab4b32b650e57f9233c1b9bd30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c5282bc1ea20767a6c092c22c761ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95c6dbe3dde6e5b84a240b2baf87201.png)
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8 . 如图,三棱柱
中,侧面
为矩形,
,
,底面
为等边三角形.
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/844b54fac727753d81a6be086330c9e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fea64ed589e56f11d34e8a1c120a08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04a2f09a6d56ce328f0fa843ef8fa89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
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2024-06-11更新
|
558次组卷
|
3卷引用:吉林省长春市东北师范大学附属中学2023-2024学年高三下学期第七次模拟考试数学试卷
名校
解题方法
9 . 已知正方体
边长为2,动点
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b93364f416d0ceadcc84387ae12e83.png)
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b93364f416d0ceadcc84387ae12e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7d4399eaa40f83220ae809bdfbddff.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-06-11更新
|
500次组卷
|
5卷引用:吉林省长春市东北师范大学附属中学2023-2024学年高三下学期第七次模拟考试数学试卷
吉林省长春市东北师范大学附属中学2023-2024学年高三下学期第七次模拟考试数学试卷江西省重点中学协作体2024届高三第二次联考数学试卷(已下线)模块5 三模重组卷 第2套 复盘卷湖北省武汉市汉铁高级中学2024届高考数学考前临门一脚试卷(已下线)立体几何与空间向量-综合测试卷B卷
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解题方法
10 . 已知矩形
,其中
,
,点D沿着对角线
进行翻折,形成三棱锥
,如图所示,则下列说法正确的是__________ (填写序号即可).
①点D在翻折过程中存在
的情况;
②三棱锥
可以四个面都是直角三角形;
③点D在翻折过程中,三棱锥
的表面积不变;
④点D在翻折过程中,三棱锥
的外接球的体积不变.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
①点D在翻折过程中存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9aabd9a42a97a1108149fafca8a919.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
③点D在翻折过程中,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
④点D在翻折过程中,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
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2024-06-10更新
|
462次组卷
|
2卷引用:吉林省长春市实验中学2023-2024学年高三下学期对位演练考试数学试卷(七)