名校
解题方法
1 . 如图所示,已知
是棱长为3的正方体,点E在
上,点F在
上,G在
上,且
,H是
的中点.
四点共面
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dfda77ecf61013170a6f43b4d9d116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d8fd9dbd9c0967145625b394f8182f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19fa4708d06d67d0cdd05294c41260e0.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc541858c196a09b464e134edf1b8261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6069dc466eec75bbeb3d5c9b51cb3a70.png)
您最近一年使用:0次
2022-09-19更新
|
1371次组卷
|
7卷引用:广东省2021年高中学业水平合格性考试模拟测数学试题
广东省2021年高中学业水平合格性考试模拟测数学试题福建省厦门双十中学2021-2022学年高一下学期期中考试数学试题(已下线)13.2.4平面与平面位置关系(1)平面与平面平行的判定与性质(备作业)-【上好课】2021-2022学年高一数学同步备课系列(苏教版2019必修第二册)(已下线)9.3 空间点、直线、平面之间的位置关系(已下线)第26讲 空间直线、平面的平行的判定4种常见方法第六章 立体几何初步 基础知识练习题——2021-2022学年高一下学期数学北师大版(2019)必修第二册山东省烟台市莱州市第一中学2023-2024学年高一下学期6月月考数学试题
名校
2 . 如图,在正方体
中,棱长为2.
;
(2)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/02a0e00113872f921116b6c0c3177d0f.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4278d42a1b5b49af9fe6d5b531fa6b7.png)
您最近一年使用:0次
2021-09-18更新
|
1771次组卷
|
7卷引用:吉林省长春市2022-2023年高二下学期基础教育质量监测数学能力抽测试题
吉林省长春市2022-2023年高二下学期基础教育质量监测数学能力抽测试题河北省张家口市2020-2021学年高一下学期期末数学试题(已下线)第8章 立体几何初步(典型30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)高一数学下学期期末全真模拟卷(1)(必修二全部内容)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)重庆市巫山县官渡中学2021-2022学年高二下学期第三次月考数学试题河北省石家庄市元氏县音体美学校2022-2023学年高一下学期期末数学试题海南省琼海市嘉积中学2023-2024学年高一下学期教学质量监测三(月考)数学试题及答案
解题方法
3 . 如图,正方体
的棱长为1,点
分别为
中点.
![](https://img.xkw.com/dksih/QBM/2020/12/21/2619078486417408/2623820449767424/STEM/f681f803-5c58-494c-9a19-4f621356668f.png?resizew=283)
(1)求证:
平面
;
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0f067a2a348ceb24a408f82992eab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b0cacb00909cf845e316fc3a00829c.png)
![](https://img.xkw.com/dksih/QBM/2020/12/21/2619078486417408/2623820449767424/STEM/f681f803-5c58-494c-9a19-4f621356668f.png?resizew=283)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b8c2721ada247b03f41f328539b301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231673dd67ab79d3c5da73904ceade1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
您最近一年使用:0次
2020-12-28更新
|
1261次组卷
|
2卷引用:福建省2021届普通高中学业水平合格性考试(会考 )适应性练习数学试卷五试题
名校
解题方法
4 . 已知
是定义在
上的奇函数.
(1)求
的值;
(2)判断
在
上的单调性,并用定义证明;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6f9b8202451375dddc577c0964d38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f7d061ccc00e8f410fc840fe7cc57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-10-22更新
|
4728次组卷
|
6卷引用:山东省2021年冬季普通高中学业水平合格性模拟考试数学试题
名校
解题方法
5 . 如图,点P为菱形ABCD所在平面外一点,PA⊥平面ABCD ,点E为PA的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/aeffbcef-be98-4d1f-800d-5437ed4896a7.png?resizew=215)
(1)求证: PC//平面BDE;
(2)求证: BD⊥平面PAC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/aeffbcef-be98-4d1f-800d-5437ed4896a7.png?resizew=215)
(1)求证: PC//平面BDE;
(2)求证: BD⊥平面PAC.
您最近一年使用:0次
2020-04-17更新
|
1496次组卷
|
3卷引用:云南省2019-2020学年1月普通高中学业水平考试数学试题
名校
解题方法
6 . 如图,四棱锥
中,底面
是正方形,
底面
.
![](https://img.xkw.com/dksih/QBM/2020/3/11/2417271005945856/2417893562458112/STEM/3ddce55118aa4ef98e36eae7960777db.png?resizew=177)
(1)求证:
平面
;
(2)若
,求点
到平面
的距离.
![](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://img.xkw.com/dksih/QBM/2020/3/11/2417271005945856/2417893562458112/STEM/3ddce55118aa4ef98e36eae7960777db.png?resizew=177)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03eb62330742830c9feea17037739dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2020-03-12更新
|
1099次组卷
|
3卷引用:贵州省2017年12月普通高中学业水平考试数学试题
名校
解题方法
7 . 如图,在正方体
中,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/1bcb982b-fed4-47d3-8108-951d17372f76.png?resizew=159)
(1)求证:
平面
;
(2)求证:
平面
.
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/1bcb982b-fed4-47d3-8108-951d17372f76.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7542b49ab149f2be8ba6b48392bef1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc78a86b12ba0b4553135a3a635fc418.png)
您最近一年使用:0次
2020-03-12更新
|
802次组卷
|
2卷引用:河南省2017年1月普通高中学业水平考试数学试题
名校
解题方法
8 . 如图,在三棱锥
中,平面
平面
,
为等边三角形,
,且
,E,F分别为AC,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/c686e2c5-6be9-4775-91ee-9d49f55350b7.png?resizew=183)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4957406b21df59fdf7fa184752287b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/c686e2c5-6be9-4775-91ee-9d49f55350b7.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
名校
9 . 已知抛物线
的焦点是
,准线是
.
(Ⅰ)写出
的坐标和
的方程;
(Ⅱ)已知点
,若过
的直线交抛物线
于不同的两点
,
(均与
不重合),直线
,
分别交
于点
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅰ)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ac1f4eb5e6145cc1b4241065218f50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0451f9e4f4db57e9ae978cdc27325698.png)
您最近一年使用:0次
解题方法
10 . 如图,
、
是以
为直径的圆上两点,
,
,
是
上一点,且
,将圆沿直径
折起,使点
在平面
的射影
在
上,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/53bb030d-135e-4660-a269-1ed1e060e3d0.png?resizew=274)
(1)求证:
⊥平面
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee6700eacd559c8820a5a5631aee02d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.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/7e77686cf448ff6cea9bfc021581da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3acee288e75061ac72203b09fce29904.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/53bb030d-135e-4660-a269-1ed1e060e3d0.png?resizew=274)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217286e225eee4d5b7a7041c027393a1.png)
您最近一年使用:0次
2020-03-16更新
|
338次组卷
|
3卷引用:河南省焦作市2014-2015学年上学期高一学业水平测试数学试卷
河南省焦作市2014-2015学年上学期高一学业水平测试数学试卷湖北省恩施州清江外国语学校2019-2020学年高二上学期期末数学试题(已下线)卷10-备战2020年新高考数学自学检测黄金10卷-《2020年新高考政策解读与配套资源》