名校
解题方法
1 . 如图所示的多面体是由底面为
的长方体被截面
所截而得到的,其中
,
,
,
.
到平面
的距离.
(2)
与平面
平行吗?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89992744fb42d976f786bbd7e562770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122ca7141c43c15c783968f5f0dbc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc90c2d45477e166b02359525f40aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89992744fb42d976f786bbd7e562770.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023高三·全国·专题练习
解题方法
2 . 已知平面
,直线AB和CD在N内的射影分别为
,
,在M内的射影分别为
,
,若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e39b6895979624b695419dd726177e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc34876d748f30fa4fc2eb6a686b5ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c94a6f24e6fae9888155f8461f878d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bfd7d66db3845617ea37cc931def500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f337f72b37efc82ffcccb5e91ec327c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
您最近一年使用:0次
名校
3 . 如图,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/cf6bbcd7-93f0-4c93-9690-813b6617f857.png?resizew=164)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a6b40391f8aa6663f20ea4f96f3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc438cb8f65c4808454520d11d885d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fd4ce957dc0d1e8740861e8910647f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/cf6bbcd7-93f0-4c93-9690-813b6617f857.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f2eae3483395cc6aca5160c64f83eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a06b68dc88cc22301870ad2819a1a2c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b41d4070854edfaa24071137b314cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f76b6ac1b8875af7156f3239dae6f7.png)
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名校
4 . 如图,在三棱柱
中,平面
平
,
,
,
.过
的平面交线段
于点E(不与端点重合),交线段BC于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/a7801a73-aa0a-466a-86bd-84c3291a31c3.png?resizew=201)
(1)求证:四边形
为平行四边形;
(2)若F为BC的中点,求直线与
与所成角的
正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002c709e9fee8d477bddfe595cc760f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/a7801a73-aa0a-466a-86bd-84c3291a31c3.png?resizew=201)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bbb740f8bc13b4be8ca4dc0aef5442.png)
(2)若F为BC的中点,求直线与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27039783266a69df2a96ea0c36cbdcd5.png)
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名校
5 . 如图,直四棱柱
中,底面
为等腰梯形,其中
,
,
,
,N为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/51be6784-d6ab-4053-92ee-9b42b259b401.png?resizew=157)
(1)若平面
交侧棱
于点P,求证:
,并求出AP的长度;
(2)求平面
与底面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cad8b2d5a892c557a5bc7650bf4dcb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4771a646e2d9895a2d4e44184ca0c558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/31/51be6784-d6ab-4053-92ee-9b42b259b401.png?resizew=157)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27ed8cad5482fe2742ef4aa65d1ddcb.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2023-11-29更新
|
405次组卷
|
2卷引用:山东省烟台市部分学校联考2023-2024学年高二上学期学业水平诊断数学试题
名校
解题方法
6 . 如图所示,多面体是由底面为
的直四棱柱被截面
所截而得到的,该直四棱柱的底面为菱形,其中
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/fa37abea-6c0c-4b50-ba26-933196123560.png?resizew=119)
(1)证明四边形
是平行四边形;并求
的长;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ada1cd3d6b1b2b559468778412ea0e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/fa37abea-6c0c-4b50-ba26-933196123560.png?resizew=119)
(1)证明四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
您最近一年使用:0次
2023·全国·模拟预测
解题方法
7 . 如图,在四棱锥
中,
,
,
是等边三角形,且
,
,
,G为
的重心.
(1)证明:
平面PCD.
(2)若
,求点C到平面PAE的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c24a968c73e960698a572ab01e3698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea8abb4cab55296ca7fc63de0af0aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/e74daa91-4337-4533-ba69-f3ae0839a5a1.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a227bcc7ee91e914c0c6bec05f82b0e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21bd7043d1e9d645183a84067144288.png)
您最近一年使用:0次
2023·全国·模拟预测
解题方法
8 . 如图,在多面体ABCDEFG中,侧面ABGF是矩形,侧面BCDG与底面EFGD是直角梯形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/670128d1-e258-4b4d-88c4-1f71087b9a39.png?resizew=178)
(1)求证:四边形ACDE是平行四边形;
(2)若
,二面角
的正切值为
,求多面体ABCDEFG的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a393ae246f050a315afd4ff4398d72d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/15/670128d1-e258-4b4d-88c4-1f71087b9a39.png?resizew=178)
(1)求证:四边形ACDE是平行四边形;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade75b6380eafafa609d94205b35a134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
9 . 如图,在三棱锥
中,
两两互相垂直,
分别为棱
的中点,
是线段
的中点,且
(1)求证:
平面
.
(2)在棱
上是否存在一点
,使得直线
与平面
所成的角为
,若存在,求线段
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2462f1dbb5a91c22f61a73993ace9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b9a4cf42189f9ef786b3c549ecd93e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55928df632fc6f2b88a44afe37e5a4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27d4e37cdd620a718e5dd741f823b81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/1c741a53-88b4-4b65-bf1d-a99a0a2ce728.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
您最近一年使用:0次
名校
10 . 如图,
,O分别是圆柱上、下底面圆的圆心,该圆柱的轴截面是边长为2的正方形ABCD,P,Q分别是其上、下底面圆周上的动点,已知P,Q位于轴截面ABCD的异侧,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/2/99f4e9b5-0314-479a-9b68-3bb5c27b0d29.png?resizew=130)
(1)当A,P,
,Q四点共面时,求
;
(2)当
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37389700fb7678d1d1ec0b5ba13e16b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/2/99f4e9b5-0314-479a-9b68-3bb5c27b0d29.png?resizew=130)
(1)当A,P,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5e1af15b01646e12b8ec729dfd0da2.png)
您最近一年使用:0次
2023-10-14更新
|
404次组卷
|
2卷引用:辽宁省沈阳市第一二〇中学2023-2024学年高二上学期第二次质量监测数学试题