名校
解题方法
1 . 如图,在四棱锥
中,已知底面
为矩形,
平面
为棱
的中点,连接
.求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
平面
;
(2)平面
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/1417f51d619f9b9f86154fdbf12e55e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c367e865cab70191ca538976d0fedde3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2024-01-11更新
|
1051次组卷
|
4卷引用:内蒙古赤峰市2021届高三上学期12月双百金科大联考数学(文)试题
内蒙古赤峰市2021届高三上学期12月双百金科大联考数学(文)试题(已下线)第07讲 空间直线﹑平面的垂直(二)-《知识解读·题型专练》(已下线)13.2.4 平面与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)江苏省宿迁市泗阳县实验高级中学2023-2024学年高一下学期第二次调研测试(5月)数学试题
名校
解题方法
2 . 如图所示,在四棱锥
中,底面
为正方形,
为侧棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/f6de2eae-ecc3-4f8e-93fd-6417f1bf9813.png?resizew=156)
(1)设经过
、
、
三点的平面交
于
,证明:
为
的中点;
(2)若
底面
,且
,求四面体
的体积.
![](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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/f6de2eae-ecc3-4f8e-93fd-6417f1bf9813.png?resizew=156)
(1)设经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(2)若
![](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/4ebbb644b9bdd7be6e7ea5722924863c.png)
您最近一年使用:0次
2021-08-09更新
|
1213次组卷
|
4卷引用:内蒙古锡林郭勒盟2024届高三上学期第二次统一考试(12月月考)(全国乙卷)文科数学试题
20-21高三下·全国·阶段练习
名校
解题方法
3 . 如图,在四棱锥
中,
平面
底面
是菱形,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/6dc927d2-a0bb-4197-8dc6-7f46d4ad4f6e.png?resizew=190)
(1)证明:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c707f0202ec1aa233e1eeacc7a4587d.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/c788746155b46628c21709a55a9f86dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/6dc927d2-a0bb-4197-8dc6-7f46d4ad4f6e.png?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36b782955ed364569d63c96e09b2430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8964550c7fc31d982b1534e884ad6f52.png)
您最近一年使用:0次
2021-05-30更新
|
1381次组卷
|
6卷引用:内蒙古包头市第四中学2021-2022学年高三上学期期中考试数学(文)试题
内蒙古包头市第四中学2021-2022学年高三上学期期中考试数学(文)试题(已下线)“超级全能生”2021届高三全国卷地区4月联考试题(甲卷)数学(文) 试题(已下线)“超级全能生”2021届高三全国卷地区4月联考试题(乙卷)数学(文) 试题陕西省2021届高三下学期教学质量检测(四)文科数学试题陕西省商洛市洛南中学2021-2022学年高三上学期第一次月考文科数学试题湖南省常德市第二中学2020-2021学年高二下学期期末数学试题
4 . 如图,在四棱维
中,底面
是边长为2的正方形,
为正三角形,且侧面
底面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8274d650-d4c3-451a-ba07-7b38b437b1f6.png?resizew=250)
(1)求证:
平面
;
(2)求二面角
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/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74837b473f275b811eae37cfd3f4bdb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8274d650-d4c3-451a-ba07-7b38b437b1f6.png?resizew=250)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8e0c5bcf2d86726cd9f561b8ff5fe.png)
您最近一年使用:0次
2021-03-25更新
|
1718次组卷
|
3卷引用:内蒙古自治区通辽新城第一中学2021届高三第三次增分训练数学(理)试题
5 . 如图几何体中,四边形
为矩形,
,
,
,
,
为
的中点,
为线段
上的一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/276cf915-641e-4a9c-af96-f51bd9b12018.png?resizew=225)
(1)证明:
面
;
(2)证明:面
面
;
(3)求三棱锥
的体积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/017af1df71f00d9c0a7fbec34cd05961.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892068c67271c00386f32a2251d97a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/613dedf2d90e58591b7ac4a250ac7b5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41d3f7d55fcbaebc4e2450ac63a3dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94febfbf27f54ed0071cb59ac52719b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/276cf915-641e-4a9c-af96-f51bd9b12018.png?resizew=225)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcafa398cc6b6079883e7ad153eb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb10d645970e5860afd3430957fab6c.png)
(2)证明:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09247d21654f0a9148dcf3232313e71c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f1d7219cd40346442b33dba84deb5c.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9644893c36173b164e9de60ee29db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
解题方法
6 . 四棱锥P﹣ABCD中,AB∥CD,AB⊥BC,AB=BC=1,PA=CD=2,PA⊥平面ABCD,E在棱PB上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/23e72e83-7552-4255-8d8c-b896597251fd.png?resizew=261)
(Ⅰ)求证:AC⊥PD;
(Ⅱ)若VP﹣ACE
,求证:PD∥平面AEC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/23e72e83-7552-4255-8d8c-b896597251fd.png?resizew=261)
(Ⅰ)求证:AC⊥PD;
(Ⅱ)若VP﹣ACE
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fed0174cd8f5b698ea9e04db6b3e45.png)
您最近一年使用:0次
2020-05-19更新
|
332次组卷
|
2卷引用:内蒙古自治区赤峰市红山区校级联考2024届高三上学期期中数学(文)试题
名校
解题方法
7 . 在四棱锥
中,
底面
,底面
是直角梯形,
,
,
,
.
(1)求证:
平面
;
(2)求证:
平面
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/5/8cc788c8-95e2-4f3a-b9d9-b27dcda8c0b8.png?resizew=280)
您最近一年使用:0次