名校
解题方法
1 . 记
的内角
所对的边分别为
,已知
.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e717c243991f038d7bc21a0fdad985b.png)
(2)若
的面积
,求
的最大值,并证明:当
取最大值时,
为直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55abde5108e7846f496584016ce82286.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e717c243991f038d7bc21a0fdad985b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a88d9c428cc72bdf012746e2781a64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2022-12-06更新
|
756次组卷
|
3卷引用:河南省洛阳市强基联盟2022-2023学年高一下学期3月月考数学试题
2 . 求证:
.
证明:因为
和
都是正数,
所以为了证明
,
只需证明
,
展开得
,即
,
只需证明
.因为
成立.
所以不等式
成立.
上述证明过程应用了( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd36577db8fa117243fb75dc7941e92.png)
证明:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c007039aaa38bfd393b5bd33024bceae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
所以为了证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd36577db8fa117243fb75dc7941e92.png)
只需证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea1c7bb4aa75d92dc6a154a8514fbb1.png)
展开得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15b5b6b15893b3cb1c60710ce3dc1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51aaf07df3b94c773de1f6caebe3864a.png)
只需证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac4705362835872eaba6e21acc9f8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cac4705362835872eaba6e21acc9f8d0.png)
所以不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd36577db8fa117243fb75dc7941e92.png)
上述证明过程应用了( )
A.综合法 | B.分析法 |
C.反证法 | D.间接证法 |
您最近一年使用:0次
2024高一下·全国·专题练习
解题方法
3 . 求证:空间四边形相邻两边中点的连线平行于经过另外两边的平面.
已知:如图,空间四边形
中,E,F分别是
,
的中点.
平面
.
已知:如图,空间四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次
2024高三·全国·专题练习
解题方法
4 . 如图,多面体
中,四边形
与四边形
均为梯形.已知点
四点共面,且
.证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dddb7e8d3e52c81162d138810af5bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621bcd3da779fc20ee56f93135a654a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd3abb3492dffd6f123a7c756bdbf53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
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解题方法
5 . 如图,在四棱锥
中,底面ABCD是矩形,
平面ABCD,M,N分别是PA,PB的中点,求证:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/2f39ff76-6743-4366-8326-8aee8785ed51.png?resizew=163)
(1)
平面ABCD;
(2)
平面PAD.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/14/2f39ff76-6743-4366-8326-8aee8785ed51.png?resizew=163)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
您最近一年使用:0次
2023-12-14更新
|
3463次组卷
|
6卷引用:新疆乌鲁木齐市第三十一中学2019-2020学年高一下学期期末考试数学试题
新疆乌鲁木齐市第三十一中学2019-2020学年高一下学期期末考试数学试题(已下线)6.5.1直线与平面垂直-【帮课堂】(北师大版2019必修第二册)湖南省邵阳市邵阳县2020-2021学年高一下学期期末数学试题2021年湖南省高中学业水平考试合格性考试仿真模拟数学试题广东省2022年普通高中学业水平考试数学模拟试题二(已下线)专题19 直线与平面的位置关系-《重难点题型·高分突破》(苏教版2019必修第二册)
2024高二·全国·专题练习
解题方法
6 . 如图,四棱锥
中,四边形
是矩形,
,
,
为正三角形,且平面
平面
,
、
分别为
、
的中点.证明:
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/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a7c298441968300f7653f59e837fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
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解题方法
7 . 已知
,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c56d479e3620d764eccab05fe0a1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e076b91a9178217532e11c496400e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8444d63d1ca92651c62fe9b220859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea730233033e2fca0bce6a369a32582f.png)
您最近一年使用:0次
解题方法
8 . 已知AB,AC分别是平面
的垂线和斜线,BC是AC在
内的射影,
且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754786a3367aca3da18ee3316e5b968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3777318aa3fbdee09cfeeea971e8fcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95e692badf11ca5ac25104a166f4467.png)
您最近一年使用:0次
解题方法
9 . 已知两条不重合的直线m,n和平面
都垂直.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0205571fa39f343ee5749b78d466bf0.png)
您最近一年使用:0次
2023高一上·全国·专题练习
10 . 求证:
=-1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b395a4143c6963a36f62b4261b9fe818.png)
您最近一年使用:0次