名校
解题方法
1 . 如图,在四棱柱
中,
底面
,底面
满足
,且
,
.
(1)求证:
平面
;
(2)求四棱锥
的体积.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991451c5002137302527700e195220e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9c270d5384dfb3a76711a595472a32.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/9/fa3d9ba1-7461-4791-bab4-eace4af09fd3.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46097478fccd7467d5b91f42c0d195a6.png)
您最近一年使用:0次
2023-08-07更新
|
628次组卷
|
4卷引用:陕西省汉中市2021届高三上学期第一次校际联考文科数学试题
陕西省汉中市2021届高三上学期第一次校际联考文科数学试题陕西省榆林市神木中学2021届高三三模文科数学试题陕西省榆林市神木中学2020-2021学年高二上学期第二次测试数学试题(已下线)第04讲 直线、平面垂直的判定与性质(五大题型)(讲义)
名校
2 . 如图,在三棱柱
中,
平面
为正三角形,侧面
是边长为2的正方形,
为
的中点.
平面
;
(2)取
的中点
,连接
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cfd6b6a7e911d10d1a4bed9ca5e749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b9a3f868837555eb40234b3375f4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
(2)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4550b5eebb311298fb89d44a913bedc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0715b04d494f97e6efe2ff694388c73.png)
您最近一年使用:0次
2023-10-13更新
|
738次组卷
|
9卷引用:陕西省汉中市2024届高三上学期第二次校际联考模拟预测理科数学试题
陕西省汉中市2024届高三上学期第二次校际联考模拟预测理科数学试题北京市第十五中学2020-2021学年高二上学期期中考试数学试题(已下线)专题09 立体几何(5大易错点分析+解题模板+举一反三+易错题通关)-2(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 专题一 空间角 微点8 二面角大小的计算综合训练【基础版】(已下线)黄金卷01北京市大峪中学2022-2023学年高二上学期期中调研数学试题四川省内江市第六中学2022-2023学年高一下学期第一次月考(创新班)数学试题(已下线)期中真题必刷基础60题(47个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
3 . 如图,在四棱锥
中,底面
为正方形,
平面
,
为
的中点,
为
与
的交点.
//平面
;
(2)求三棱锥
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e076b62ef0f326e366b6d366d68812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90deda6e128fade762bdb3b74bedf511.png)
您最近一年使用:0次
2023-10-12更新
|
953次组卷
|
12卷引用:内蒙古包头市第四中学2020-2021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2020-2021学年高三上学期期中考试数学(文)试题陕西省延安市子长市中学2021-2022学年高三上学期第一次月考文科数学试题陕西省汉中市2024届高三上学期第二次校际联考模拟预测文科数学试题甘肃省张掖市高台县第一中学2022-2023学年高三上学期开学考试数学(文)试题陕西省汉中市2020-2021学年高二下学期期中联考文科数学试题陕西省宝鸡市千阳县2022-2023学年高二下学期期中文科数学试题(已下线)考点8 平行的判定与性质 2024届高考数学考点总动员【练】上海市金山区2024届高三上学期质量监控数学试题广西柳州市第三中学2021-2022学年高二4月月考数学(文)试题广东省茂名市电白区2021-2022学年高一下学期期中数学试题广西“贵百河”2023-2024学年高二上学期12月新高考月考测试数学试题(已下线)重难点专题10 轻松解决空间几何体的体积问题-【帮课堂】(苏教版2019必修第二册)
解题方法
4 . 如图,在三棱柱
中,
平面
,且
,点
是棱
的中点.
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cd9a2cf5917a7487640ee921762071d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/10/5ae7b0c0-0c74-4694-b889-ecfa3bdb385e.png?resizew=145)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a98287a302228ece1fa53c5c66c590f.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efebbbd5803c8775e30bbb27ad68719e.png)
您最近一年使用:0次
名校
解题方法
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
;
(3)求三棱锥
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/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/30067b7b236d17af8a462f96a58d11bd.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)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e73fe210736ce7b30b039d34587e3c1.png)
您最近一年使用:0次
2024-05-12更新
|
3308次组卷
|
8卷引用:陕西省商洛市洛南中学2024届高三第十次模拟预测文科数学试题
陕西省商洛市洛南中学2024届高三第十次模拟预测文科数学试题【全国市级联考】北京市西城区2017-2018学年高一下学期期末考试数学试题江苏省南通市2019-2020学年高二上学期期初调研测试数学试题北京市第八中学2020-2021学年高二下学期期末数学试题北京市陈经纶中学2023-2024学年高一下学期期中练习数学试卷(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)(已下线)核心考点5 立体几何中的位置关系 B提升卷 (高一期末考试必考的10大核心考点)广东省深圳市深圳大学附属中学、龙城高级中学第二次段考2023-2024学年高一下学期5月月考数学试题
解题方法
6 . 在四棱锥
中,底面
是正方形,AC与BD交于点O,
底面
,F为BE的中点.
(1)求证:
平面ACF;
(2)求证:
;
(3)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f09ad78d4eccd1a9c9ccd3c4af79c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/5/3cd1d596-375b-47e9-9a87-8dd43d44b8b1.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84be64d28b1623e71ad989f37336b1f2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abcda8cc3300d88a90f5c3b463ec877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c416b5f18fbb0b7f79e8a5702acd13.png)
您最近一年使用:0次
2023-08-03更新
|
491次组卷
|
4卷引用:陕西省榆林市第二中学2019-2020学年高三上学期11月月考数学(文)试题
陕西省榆林市第二中学2019-2020学年高三上学期11月月考数学(文)试题第 11 章 简单几何体 综合测试【3】(已下线)专题07锥体(6个知识点9种题型1种高考考法)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)(已下线)第11章 简单几何体(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
解题方法
7 . 如图,几何体ABCDEF中,矩形CDEF所在平面与梯形ABCD所在平面互相垂直,
,
,
,H为AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/1614a761-2f7a-4831-b0cf-94b0561f517b.png?resizew=123)
(1)证明:平面
平面CFH;
(2)若几何体ABCDEF的体积为4,求CF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08062a925efb07c38a229b8628e3b41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/1614a761-2f7a-4831-b0cf-94b0561f517b.png?resizew=123)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f3e3f310f6ec3f3a26498e7ee17a00.png)
(2)若几何体ABCDEF的体积为4,求CF.
您最近一年使用:0次
名校
解题方法
8 . 如图,在四棱锥P﹣ABCD中,
PAB是边长为2的等边三角形.梯形ABCD满足BC=CD=1,AB∥CD,AB⊥BC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1a768634-a473-45ca-95fe-2e447f201c0a.png?resizew=149)
(1)求证:PD⊥AB;
(2)若PD=2,求点D到平面PBC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1a768634-a473-45ca-95fe-2e447f201c0a.png?resizew=149)
(1)求证:PD⊥AB;
(2)若PD=2,求点D到平面PBC的距离.
您最近一年使用:0次
2022-09-21更新
|
667次组卷
|
5卷引用:2020届清华大学中学生标准学术能力诊断性测试高三5月测试数学(文)试题(一卷)
解题方法
9 . 如图,矩形
所在平面垂直于直角
所在平面,
,
,
,点
在
上且
,
为
的中点,
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/e253f2a8-607b-4ad6-8e63-ca2eb38d44fe.png?resizew=138)
(1)证明:
平面
;
(2)若三棱锥
的体积为
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c013bbe1fb6e9acf461548b5cf6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdf23e73ae2a15c04bbed3981cb8e511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/2/e253f2a8-607b-4ad6-8e63-ca2eb38d44fe.png?resizew=138)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a20ea69475dcf57a5ff18c13eceaaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a8898c347a62c7de2bdca3f3c7e33.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5e84059306d1173e38fe3437cc13daf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,已知多面体
中,
,
,
均垂直于平面
.
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815048579457024/2815220150419456/STEM/9ef861cc-ef82-4047-b39d-7e4210154f4a.png?resizew=206)
(I)证明:
平面
;
(II)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a2749f3f4224a1753bcbe2e13b88fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef4d07ca8645539b455e196a305d6.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815048579457024/2815220150419456/STEM/9ef861cc-ef82-4047-b39d-7e4210154f4a.png?resizew=206)
(I)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1068ada1763c76ec2121dfa32bf0fe38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(II)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
您最近一年使用:0次
2021-09-24更新
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414次组卷
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4卷引用:陕西省咸阳市高新一中2022-2023学年高三上学期第三次质量检测文科数学试题