阅读下列材料,完成相应任务.
【探究三角形中边与角之间的不等关系】
学习了等腰三角形,我们知道在一个三角形中,等边所对的角相等;反过来,等角所对的边也相等,那么,不相等的边所对的角之间的大小关系怎样呢?大边所对的角也大吗?下面是奋进小组的证明过程.
如图1,在△
中,已知
.求证
.
![](https://img.xkw.com/dksih/QBM/2022/10/15/3088002471641088/3089693671415808/STEM/d033c0b3b9554055851196a8ce9611f0.png?resizew=298)
证明:如图2,将△
折叠,使边
落在
上,点
落在
上的点
处,折痕
交
于点
.则
.
∵
________
(三角形外角的性质)
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b487f865bfb4750eee61bf9ec5059f.png)
∴
(等量代换)
类似地,应用这种方法可以证明“在一个三角形中,大角对大边,小角对小边”的问题.
(1)任务一:将上述证明空白部分补充完整;
(2)任务二:上述材料中不论是由边的不等关系,推出角的不等关系,还是由角的不等关系推出边的不等关系,都是转化为较大量的一部分与较小量相等的问题,再用三角形外角的性质或三边关系进而解决,这里主要体现的数学思想是________;(填正确选项的代码:单选)
A.转化思想 B.方程思想 C.数形结合思想
(3)任务三:根据上述材料得出的结论,判断下列说法,正确的有________(将正确的代码填在横线处:多选).
①在△
中,
,则
;
②在△
中,
,
,则△
是锐角三角形;
③
△
中,
,则最长边是
;
④在△
中,
,
,则
.
【探究三角形中边与角之间的不等关系】
学习了等腰三角形,我们知道在一个三角形中,等边所对的角相等;反过来,等角所对的边也相等,那么,不相等的边所对的角之间的大小关系怎样呢?大边所对的角也大吗?下面是奋进小组的证明过程.
如图1,在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5bac918d34537ff02a518a63031aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaae5a489951101a9c06fd94ff523d6.png)
![](https://img.xkw.com/dksih/QBM/2022/10/15/3088002471641088/3089693671415808/STEM/d033c0b3b9554055851196a8ce9611f0.png?resizew=298)
证明:如图2,将△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77936a859f39507de5a2d3070b13a60a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289d7a880379d6060065c829b45b0ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3256a9f3b49b8e60ce44e8deec42d822.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b28daad9a051987ab64dc8a299d42bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66cb5797ef6c0853368ca92df9e5402b.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b487f865bfb4750eee61bf9ec5059f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaae5a489951101a9c06fd94ff523d6.png)
类似地,应用这种方法可以证明“在一个三角形中,大角对大边,小角对小边”的问题.
(1)任务一:将上述证明空白部分补充完整;
(2)任务二:上述材料中不论是由边的不等关系,推出角的不等关系,还是由角的不等关系推出边的不等关系,都是转化为较大量的一部分与较小量相等的问题,再用三角形外角的性质或三边关系进而解决,这里主要体现的数学思想是________;(填正确选项的代码:单选)
A.转化思想 B.方程思想 C.数形结合思想
(3)任务三:根据上述材料得出的结论,判断下列说法,正确的有________(将正确的代码填在横线处:多选).
①在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df19eae422a11ecd874c01ce3d68178e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1494d156b2751301baf97ca7746cc971.png)
②在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69d51f1998b6335cc7323b37537c251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d36d0c89e9b5abbe28a7dad2468ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7eccdc904f71a7a6a02134f47e08072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9429e394d7cf08f2cdbc7f1be7dfaaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
④在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aca429d9688fa2721280ae7d7a00b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a691a85ae5a0bc49d3c411926ee1cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63dee45a1084de33934b9abb6bed96ad.png)
更新时间:2022-10-17 16:20:46
|
相似题推荐
解答题-问答题
|
适中
(0.65)
【推荐1】如图,在△ABC中,已知点D、E、F分别在边BC、AC、AB上,且FD=ED,BF=CD,∠FDE=∠B,那么∠B和∠C的大小关系如何?为什么?
解:因为∠FDC=∠B+∠DFB ,
即∠FDE+∠EDC=∠B+∠DFB.
又因为∠FDE=∠B(已知),
所以∠ =∠ .
在△DFB和△EDC中,
所以△DFB≌△EDC .
因此∠B=∠C.
解:因为∠FDC=∠B+∠DFB ,
即∠FDE+∠EDC=∠B+∠DFB.
又因为∠FDE=∠B(已知),
所以∠ =∠ .
在△DFB和△EDC中,
所以△DFB≌△EDC .
因此∠B=∠C.
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987882259324928/2988973357932544/STEM/d2f13a5cbdea4df79a5e4bdc199fcfc2.png?resizew=172)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐2】如图,在△ABC中,点D在BC上,AB=AC=BD,AD=DC,将△ACD沿AD折叠至△AED,AE交BC于点F.
(1)求∠C的度数;
(2)求证:BF=CD.
(1)求∠C的度数;
(2)求证:BF=CD.
![](https://img.xkw.com/dksih/QBM/2019/4/12/2180750184194048/2181436733284352/STEM/a27f7b954f8d4bc8abdcdc7a6a9746cf.png?resizew=145)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
名校
【推荐1】如图,在
中,
,把
沿直线
折叠,点A与点B重合.
,则
的度数为 ;
(2)若
,
,求
的长;
(3)当
的周长为m(
),
,求
的面积.(用含m、n的代数式表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010fd1407b94f9057f5a07b6d9d43cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81742df308d663ebbce0b6818555767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633ad41d6acbcebac5e7c7ac1724ec14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
【推荐1】如图,在
中,
平分
是
上一点,
,
交
于点
,交
的延长线于点
,
交
的延长线于点
.
是等腰三角形;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4fbca156a5cc929934f3fb411c3243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024dc2ccbbe321774df5d44e8785b203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d354155f71a1736c1c9186168695edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5837d15f8e3aa145ec2587e9447b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceff3844281849df3e37a2e56e110549.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91ac38719ac70e0597a72e7f0deceac.png)
您最近一年使用:0次
解答题-作图题
|
适中
(0.65)
名校
【推荐2】已知:如图,线段AB和射线BM交于点B.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/18/0471762e-fd2b-4a8a-95cf-d8fa8bd3a1d1.png?resizew=134)
(1)利用尺规完成以下作图,并保留作图痕迹.(不要求写作法)
①在射线BM上求作一点C,使AC=AB;
②在线段AB上求作一点D,使点D到BC,AC的距离相等;
(2)在(1)所作的图形中,若∠ABM=72°,则图中与BC相等的线段是 .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/18/0471762e-fd2b-4a8a-95cf-d8fa8bd3a1d1.png?resizew=134)
(1)利用尺规完成以下作图,并保留作图痕迹.(不要求写作法)
①在射线BM上求作一点C,使AC=AB;
②在线段AB上求作一点D,使点D到BC,AC的距离相等;
(2)在(1)所作的图形中,若∠ABM=72°,则图中与BC相等的线段是 .
您最近一年使用:0次