已知:线段AB.
,使得
,
.
作法:
①分别以点A和点B为圆心,AB长为半径作弧,两弧交于点D;
②连接BD,在BD的延长线上截取
;
③连接AC.
则
为所求作的三角形.
(1)使用直尺和圆规,依作法补全图形(保留作图痕迹);
(2)完成下面的证明.
证明:连接AD.
∵
,
∴
为等边三角形( ).(填推理的依据)
∴
.
∵
,
∴
.
∴
__________( ).(填推理的依据)
∴
.
∴
.
在
中,
∴
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e744f480e11f588570c5d6738799f5.png)
作法:
①分别以点A和点B为圆心,AB长为半径作弧,两弧交于点D;
②连接BD,在BD的延长线上截取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0145eeb463f49ec362d52ef68dab367.png)
③连接AC.
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)使用直尺和圆规,依作法补全图形(保留作图痕迹);
(2)完成下面的证明.
证明:连接AD.
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf8ddc214299072a601993b8db4558a.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d4254fa89df60477efb9910fb77122c.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b7513e09cccf40c3a483064b97e48.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064c359bafcd1841d582707419d1ac2d.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/775f25d670568b19485ec92fb199d981.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e744f480e11f588570c5d6738799f5.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfad30e54fa46823d28b002e12161d26.png)
2022·北京东城·一模 查看更多[11]
2022年北京市东城区中考一模数学试题(已下线)专题10 尺规作图与几何初步——5年(2018~2022)中考1年模拟数学分项汇编(北京专用)北京市第一六六中学2022-2023学年八年级上学期期中考试 数学试题(已下线)专题1.1 等腰三角形(知识讲解)-2022-2023学年八年级数学下册基础知识专项讲练(北师大版)北京市西城区北京师范大学附属实验中学2022~2023学年九年级下学期数学统一练习(一)北京市广渠门中学2022~2023学年九年级下学期第一次质量检测数学试题(已下线)数学(北京卷)-学易金卷:2023年中考第一次模拟考试卷2023年北京市东城区广渠门中学中考一检数学试卷山东省龙口市(五四制)2022-2023学年七年级下学期期末数学试题内蒙古自治区赤峰市红山区2022-2023学年九年级下学期4月月考数学试题2023年内蒙古赤峰市红山区中考数学模拟预测题
更新时间:2022-05-23 14:25:34
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