解题方法
1 . 如图,在四棱锥
中,底面ABCD为等腰梯形,
,
,E为AP的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/24/ea8f4798-8e8d-4286-9de4-f01aa876143c.png?resizew=157)
(1)证明:
平面PBC.
(2)求四棱锥
外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05ef25a6b40700f28f81782b1c3b9d2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/24/ea8f4798-8e8d-4286-9de4-f01aa876143c.png?resizew=157)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
您最近一年使用:0次
2022-08-23更新
|
379次组卷
|
3卷引用:河南省豫西名校2022-2023学年高二上学期开学考试数学试题
名校
解题方法
2 . 在三棱锥
中,
,
,
、
分别是棱
、
的中点.
;
(2)线段
上是否存在点
,使得
平面
?若存在,指出点
的位置;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/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbbe7f48676298f2ee0cb1901992eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
2022-09-29更新
|
962次组卷
|
9卷引用:河南省南阳市第一中学校2023届高三上学期第三次阶段性测试文科数学试题
河南省南阳市第一中学校2023届高三上学期第三次阶段性测试文科数学试题宁夏石嘴山市平罗中学2022-2023学年高二上学期第一次月考数学(理)试题(A)浙江省金华市曙光学校2022-2023学年高二上学期10月第一次阶段考试数学试题(已下线)专题8-4 非建系型:探索性平行与垂直证明及求角度(已下线)8.6.2直线与平面垂直的性质定理(第2课时)(精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)第29讲 线面垂直证线线平行和垂直2种题型(已下线)立体几何专题:立体几何探索性问题的8种考法陕西省西安市长安区第一中学2022-2023学年高一下学期5月月考数学试题(已下线)专题突破:空间几何体的动点探究问题-同步题型分类归纳讲与练(人教A版2019必修第二册)
解题方法
3 . 如图,四边形ABCD是正方形,O是正方形的中心,
底面ABCD,E是PC的中点,Q是线段PC上的任意一点.求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/520050f8-cbca-4544-94f1-39529753158e.png?resizew=252)
(1)
平面BDE;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/520050f8-cbca-4544-94f1-39529753158e.png?resizew=252)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f844a41f79ea2b231b326f8633beac50.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a228ca9989e2318ed79b5a2c76cb48.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在三棱柱
中,侧面
底面
,
,
,且
,
为
中点.
![](https://img.xkw.com/dksih/QBM/2022/8/25/3052106803642368/3058231501807616/STEM/fcc2dcadb93e4ee5970fa6e1bd364e7a.png?resizew=288)
(1)求证
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb88c278e18d776f165bc571031071d8.png)
(2)在
上是否存在一点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
平面
,若不存在,说明理由;若存在,确定点E的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58bd6407cc044990cc765df9e710369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2022/8/25/3052106803642368/3058231501807616/STEM/fcc2dcadb93e4ee5970fa6e1bd364e7a.png?resizew=288)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb88c278e18d776f165bc571031071d8.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc9ffc43a56921fe79f8602636b8b0f.png)
您最近一年使用:0次
2022-09-03更新
|
560次组卷
|
3卷引用:河南省洛阳市洛宁一高祥云联考2022-2023学年高二上学期8月阶段性考试数学试题
河南省洛阳市洛宁一高祥云联考2022-2023学年高二上学期8月阶段性考试数学试题河南省禹州市北大公学禹州国际学校2022-2023学年高二上学期开学考试数学试题(已下线)专题6-3立体几何大题综合归类-1
5 . 在三棱台
中,
平面ABC,AB⊥BC,且
,O为AC的中点,P是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/c8ed057a-0528-4034-80d1-2b5657b87e5d.png?resizew=174)
(1)证明:平面
平面POB.
(2)若AB=4,求P到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee6a2c9d3843855bf89516bdd6ad5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb410774f7d4f94e3bded41f0e09e7fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/14/c8ed057a-0528-4034-80d1-2b5657b87e5d.png?resizew=174)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
(2)若AB=4,求P到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6a51a168f6a3c308fcfcede6406aa3.png)
您最近一年使用:0次
解题方法
6 . 如图,四棱锥
的底面ABCD是正方形,
平面ABCD,
,E是SD上的点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/e4e0efc5-896e-488f-8b66-c642efc53878.png?resizew=171)
(1)求证:
;
(2)若点B到平面ACE的距离为
,求实数
的值.
![](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/8d934ab4f312fc2fa5b53d68ac2fd6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5940069ecb7f22cca04d1d386af5def.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/e4e0efc5-896e-488f-8b66-c642efc53878.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)若点B到平面ACE的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b234f945df3ebb9fe5e3e903fad696b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
7 . 在如图所示的几何体中,四边形ABCD是正方形,平面ABCD⊥平面PAB,E,F分别是线段AD,PB的中点,
.证明:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/ceee8839-7f73-4488-9191-c59704a48bfc.png?resizew=158)
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面PDC;
(2)PB⊥平面DEF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/ceee8839-7f73-4488-9191-c59704a48bfc.png?resizew=158)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
(2)PB⊥平面DEF.
您最近一年使用:0次
2022-07-08更新
|
623次组卷
|
5卷引用:河南省名校联盟2022-2023学年高二上学期开学考试数学试题
河南省名校联盟2022-2023学年高二上学期开学考试数学试题湖北省鄂州市2021-2022学年高一下学期期末数学试题黑龙江省绥化市望奎县第一中学2021-2022学年高一下学期期末数学试题(已下线)7.2 空间几何中的垂直(精练)(已下线)7.1 空间几何中的平行与垂直(精讲)
解题方法
8 . 如图,在棱长为
的正方体
中,
、
分别为棱
、
的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/4/3015415316135936/3016275007193088/STEM/f422db84b1db4a258a7691963d857941.png?resizew=227)
(1)证明:平面
平面
;
(2)求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2022/7/4/3015415316135936/3016275007193088/STEM/f422db84b1db4a258a7691963d857941.png?resizew=227)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28b7860d15b6c3532ff829bc6eca43b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
2022-07-05更新
|
1906次组卷
|
9卷引用:河南省南阳地区2021-2022学年高一下学期期终摸底考试数学试题
9 . 如图所示,圆锥PO的母线长为
,底面圆O的直径AB=2,C是圆O所在平面内一点,AC与圆O相切,连接BC交圆O于点D,连接PD,PC,CO,DO.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/d84a27cd-a4b4-4940-aa25-f278bb74b828.png?resizew=237)
(1)证明:
平面PAC;
(2)若
,求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/d84a27cd-a4b4-4940-aa25-f278bb74b828.png?resizew=237)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069bce57ad755d2340de357a67b8ae07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7c452c79a3dcb02718fe9e9b3feb64.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,矩形
所在平面与半圆弧
所在平面垂直,M是
上异于C,D的点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/c35bff93-6a8a-41ce-8715-afd6132a8212.png?resizew=180)
(1)证明:
平面
;
(2)在线段
上是否存在点P,使得
平面
?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/7/c35bff93-6a8a-41ce-8715-afd6132a8212.png?resizew=180)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3219a5fbe920e617eff32e558c0c6ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2022-07-05更新
|
910次组卷
|
7卷引用:河南省驻马店市新蔡县第一高级中学2021-2022学年高二下学期7月月考文科数学试题
河南省驻马店市新蔡县第一高级中学2021-2022学年高二下学期7月月考文科数学试题江西省萍乡市2021-2022学年高一下学期期末考试数学试题(已下线)7.2 空间几何中的垂直(精练)(已下线)9.3 空间点、直线、平面之间的位置关系(已下线)立体几何专题:立体几何探索性问题的8种考法(已下线)专题强化一 线面、面面的平行和垂直位置关系-《考点·题型·技巧》(已下线)高一下期末真题精选(基础60题60个考点专练)