1 . 如图,在四棱锥
中,
平面ABCD,底面ABCD为正方形,
,E,F分别为PD,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/0bd44357-ca0f-45c5-8a87-77a82472215e.png?resizew=143)
(1)求证:
平面PAD;
(2)求平面AEF与底面ABCD所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b10835116b9b777a666b438c907b49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/0bd44357-ca0f-45c5-8a87-77a82472215e.png?resizew=143)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
(2)求平面AEF与底面ABCD所成角的余弦值.
您最近一年使用:0次
名校
2 . 如图,在四棱台
中,底面
是边长为2的菱形,
,平面
平面
,点
分别为
的中点,
均为锐角.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/728a0186-2b6c-4c2e-9b54-f74aa2b56c10.png?resizew=225)
(1)求证:
;
(2)若异面直线
与
所成角正弦值为
,四棱锥
的体积为1,求二面角
的平面角的余弦值.
![](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/cd7a42341edbc0b01ab0769c4c02c3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9578aee1ffa7a74c04debf1679b068d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cef469b1ee29d124cfd6f62423724cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6b28373d1cf44efd0301e8cbf16080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a046c94d66691601bd10ce823fd26629.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/728a0186-2b6c-4c2e-9b54-f74aa2b56c10.png?resizew=225)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1de5964353beb55c5058b2a431eecaf.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2e341788ce1be913bc47b3831c6baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1654dfe63f11563eadbaee32dae7b1e.png)
您最近一年使用:0次
2022-11-24更新
|
3191次组卷
|
11卷引用:吉林省长春市第二实验中学2022-2023学年高三上学期期末数学试题
吉林省长春市第二实验中学2022-2023学年高三上学期期末数学试题浙江省稽阳联谊学校2022-2023学年高三上学期11月联考数学试题 四川省成都市锦江区嘉祥外国语高级中学2022-2023学年高一下学期期末考试数学试题重庆市2023届高三上学期期中数学试题(已下线)专题08 立体几何解答题常考全归类(精讲精练)-2(已下线)专题3 解答题题型广东省揭阳市普宁国贤学校2023届高三下学期3月连考3数学试题浙江省金华市东阳市外国语学校、东阳中学2022-2023学年高一下学期5月联考数学试题(已下线) 第1章 空间向量与立体几何单元测试能力卷-2023-2024学年高二数学上学期人教A版(2019)选择性必修第一册(已下线)专题15 立体几何解答题全归类(练习)(已下线)上海市奉贤区2024届高三一模数学试题变式题16-21
名校
解题方法
3 . 已知a,b,c分别为△ABC内角A,B,C的对边,且
.
(1)证明:
;
(2)若△ABC的面积S=2,
,求角C.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a071b3271a35bf3eae29c9c774820333.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c45c4afdb30512752c377037e4c71e9.png)
(2)若△ABC的面积S=2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af039cad52ca4e1f1e322277bc81afd.png)
您最近一年使用:0次
4 . 已知抛物线
的焦点为
,
为抛物线上一点,
,且
的面积为
,其中
为坐标原点.
(1)求抛物线
的方程;
(2)已知点
,不垂直于
轴的直线
与抛物线
交于
,
两点,若直线
,
关于
轴对称,求证:直线
过定点并写出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6595367508aef224945bb140eae7bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0942fc5e4da4ae86721efc5bb7e2cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23728b4c0467a27d90f71b424f6a946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-19更新
|
450次组卷
|
5卷引用:吉林省白城市通榆县2022-2023学年高二上学期期末数学试题
名校
解题方法
5 . 已知椭圆
的一个顶点为
,离心率为
.过椭圆右焦点且斜率为
的直线
与椭圆相交于两点
,
,与
轴交于点
,线段
的中点为
,直线
过点
且垂直于
(其中
为原点).
(1)求椭圆的标准方程并求弦
的长;
(2)证明直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7968194cf13e872ab941231cfc9eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆的标准方程并求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-01-15更新
|
296次组卷
|
3卷引用:吉林省延边朝鲜族自治州敦化市实验中学校2022-2023学年高二上学期期末数学试题
6 . 如图,四棱锥
的底面ABCD是边长为2的正方形,平面
平面ABCD,
是斜边PA的长为
的等腰直角三角形,E,F分别是棱PA,PC的中点,M是棱BC上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/30/89f91959-8a4f-4168-aacd-4578160076f7.png?resizew=172)
(1)求证:平面
平面PBC;
(2)若直线MF与平面ABCD所成角的正切值为
,求锐二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/30/89f91959-8a4f-4168-aacd-4578160076f7.png?resizew=172)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f165b7e8c4d8d5e028b8ffd8f0d26a49.png)
(2)若直线MF与平面ABCD所成角的正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dedfba8b9447a4db53baae62fdeebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbb52befa94a9f54e6f3e3125918016.png)
您最近一年使用:0次
2023-01-14更新
|
344次组卷
|
2卷引用:吉林省长春市长春外国语学校2022-2023学年高三上学期期末数学试题
名校
解题方法
7 . 已知等差数列
满足
,
,
的前n项和为
.
(1)求
及
的通项公式;
(2)记
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0939caf47d751f8c7139bd0b25fe98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5775fff251847305756b90e62429f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1339f4e85f82a007362def9c8a31237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762022cd7c3133845e5f6c5cbb6c536c.png)
您最近一年使用:0次
2023-01-14更新
|
501次组卷
|
3卷引用:吉林省长春市长春外国语学校2022-2023学年高三上学期期末数学试题
名校
解题方法
8 . 如图,四面体ABCD中,O,E分别是BD,BC的中点,CA=CB=CD=BD=2,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/e2c85236-8f8d-40b5-9744-a9381c8d2e86.png?resizew=200)
(1)求证:
平面BCD;
(2)求点E到平面ACD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65d5853c26657db448af610ac72cca4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/e2c85236-8f8d-40b5-9744-a9381c8d2e86.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce03b310edce42191f9fa75a1c909ac.png)
(2)求点E到平面ACD的距离.
您最近一年使用:0次
2022-12-17更新
|
959次组卷
|
7卷引用:吉林省四平市第一高级中学2021-2022学年高三上学期期末考试数学(文)试题
吉林省四平市第一高级中学2021-2022学年高三上学期期末考试数学(文)试题河南省郑州市励德双语学校2022-2023学年高三上学期期末考试文科数学试题山西省大同市博盛中学2022-2023学年高二下学期期末数学试题(已下线)8.6.2直线与平面垂直的判定定理(第1课时)(精练)-【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)8.6.2直线与平面垂直的判定定理(第1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)微专题17 空间中的五种距离问题(1)(已下线)8.6.2 直线与平面垂直(1) -2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)
9 . 已知直三棱柱
中,
,D为AB中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/aeec781d-2087-408e-a868-c39d76337b26.png?resizew=162)
(1)求证:
平面
;
(2)求三棱锥
的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cad7b03f934718b18ce34cdf0b85863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c279c8033acb94c3f91be2e05b0a6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8475da4df2025924d60ad1a2e38d86.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/2/aeec781d-2087-408e-a868-c39d76337b26.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcecfc88e45465b7e2215a8557148da.png)
您最近一年使用:0次
10 . 如图,四棱锥
中,
平面
,PB与底面所成的角为45°,底面
直角梯形,
,
.
![](https://img.xkw.com/dksih/QBM/2022/7/14/3022237506609152/3023158088261632/STEM/55c24aa8300d4d7eb583e60770eac054.png?resizew=193)
(1)求证:平面
平面
;
(2)若E为PD的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/405effb49ef901476701e72cc47918da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c08d002130408631a5bb81f09ccef494.png)
![](https://img.xkw.com/dksih/QBM/2022/7/14/3022237506609152/3023158088261632/STEM/55c24aa8300d4d7eb583e60770eac054.png?resizew=193)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若E为PD的中点,求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7628ad58e0832bbf636e04be8b9cbfe.png)
您最近一年使用:0次