解题方法
1 . 已知直四棱柱
的底面为梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f693ef548c754390e1ae722de76cbb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,若
平面
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f693ef548c754390e1ae722de76cbb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a704cdc66c39bfacf66e861dffefe8b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b449ce3e78881defc7a72104a7b38c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dbcc81f7bc35bf09e4d1c0490d512b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6243490cdfc0747c0cba492bd78a0758.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-04-07更新
|
278次组卷
|
2卷引用:河南省濮阳市2024届高三下学期第一次模拟考试数学试题
名校
2 . 如图,在四棱锥
中,底面
是平行四边形,
、
分别为
、
上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/1be74814-b430-4931-b6d0-764847974183.png?resizew=166)
(1)证明:
平面
;
(2)若
平面
,
为
的中点,
,
,求二面角
的正切值.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5a5af5960e1ac65946343889f69857.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/1be74814-b430-4931-b6d0-764847974183.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9068f29d671d76d1e95ba3a4eaff5b96.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3294cff9c742de2d2cee7472138eb363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baa2f1a925d67fcd406218b83015d13.png)
您最近一年使用:0次
2024-03-25更新
|
793次组卷
|
2卷引用:江苏省南京市六校2024届高三下学期期初联合调研数学试题
解题方法
3 . 已知正方体的棱长为3,垂直于棱
的截面分别与面对角线
,
相交于点
,则四棱锥
体积的最大值为
您最近一年使用:0次
名校
4 . 如图,在四棱锥
中,
平面
为矩形,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/743255c0-9212-4e41-86ab-3908432a857e.png?resizew=136)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
.
(2)若
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654c6391665a5aee872901309abd4b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044fc06badbda5c3f7882af087e8ce9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/743255c0-9212-4e41-86ab-3908432a857e.png?resizew=136)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585b9bbafa936929b1e77fe38b8ef4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
解题方法
5 . 如图,多面体
是由三棱柱
截去部分后而成,D是
的中点.
(1)若
平面
,求点C到平面
的距离;
(2)如图,点E在线段
上,且
,点F在
上,且
,问
为何值时,
∥平面
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e3ff5b7a53ef89d72fbc2cef3cbdbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/11/aecf3969-a8c1-45d6-80d3-927621b48bc9.png?resizew=159)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1a99ed62d0daa3dee3c2833d2e1c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535a3700e6d20d0beefaae8f57dea2e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dddfef906818cc8ddd00f867b77f227.png)
(2)如图,点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3696f3ae3de7529611929d0b4e7b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf825bea2da10773df06c70624e64c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dddfef906818cc8ddd00f867b77f227.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,正方体
的棱长为
,
、
是线段
上的两个动点,且
,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/6f3c6462-7def-423f-a2f9-8a29cc0ccc16.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f115f2683c0422042f1846450885e7fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/6f3c6462-7def-423f-a2f9-8a29cc0ccc16.png?resizew=158)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.三棱锥![]() |
您最近一年使用:0次
名校
解题方法
7 . 如图,在四棱锥
中,底面
为矩形,侧面
底面
,侧棱
和侧棱
与底面
所成的角均为
,
,
为
中点,
为侧棱
上一点,且
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/2b4b68ee-7d40-407e-9ab1-a79d6224add0.png?resizew=144)
(1)请确定点
的位置;
(2)求平面
与平面
所成夹角的余弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132fc900a3e6678ee9854599ad6bfd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a04ea8ebc597fd1f5d6bb8df181a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/2b4b68ee-7d40-407e-9ab1-a79d6224add0.png?resizew=144)
(1)请确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f87bc10632de183256edc87c82f8382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2024-02-08更新
|
660次组卷
|
3卷引用:山东省青岛第二中学2024届高三下学期期初阶段性练习数学试题
名校
8 . 如图,在直三棱柱
中,
分别为
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(2)若点
是棱
上一点,且直线
与平面
所成角的正弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9566510295543eeac41ec809a3df639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4dfea6353fc25e88535e865a4982cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
您最近一年使用:0次
2024-01-19更新
|
955次组卷
|
4卷引用:广东省深圳中学2023-2024学年高三寒假开学适用性考试数学试题
(已下线)广东省深圳中学2023-2024学年高三寒假开学适用性考试数学试题北京市门头沟区大峪中学2023-2024学年高二下学期开学考试数学试题北京市东城区2024届高三上学期期末统一检测数学试题宁夏吴忠市2024届高三下学期高考模拟联考试卷(二)理科数学试题
名校
解题方法
9 . 已知
是平面
上的点,
是平面
上的点,且
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ab061ed9ec918926f1defceb85924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18b383fa3ea6598d7216944fea12ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b303b1f07604f5303aea94df7f0518e9.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-01-18更新
|
491次组卷
|
3卷引用:广东省中山市中山纪念中学2024届高三下学期开学模拟测试数学试题(一)
名校
10 . 已知
,
是两条不同的直线,
,
是两个不同的平面,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() | D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-06-14更新
|
259次组卷
|
2卷引用:吉林省四平市第一高级中学2023-2024学年高二上学期期初验收考试数学试题