1 . ●问题发现
如图1,
和
都是等边三角形,边
和
在同一直线上,
是边
的中点,
,连接
,则下列结论正确的是__________.(填序号即可)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/b62eb049-7dac-45cb-bcbb-eb9449b02b3b.png?resizew=825)
①
;②
;③
;④整个图形是轴对称图形.
●数学思考
将图1中的
绕着点
旋转,
不动,连接
和
,如图2,则
和
具有怎样的数量和位置关系?请给出证明过程;
●拓展应用
已知
,
,在图1中的
绕着点
旋转的过程中,当
时,求线段
的长度.
如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805768a5ffaf8bdfa4bc3b680aafdc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/b62eb049-7dac-45cb-bcbb-eb9449b02b3b.png?resizew=825)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf2e3236ea30ee2c37928b98041f13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c503e29373e8d87134bdb46bd3912910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4151e948feebdf7b91fbe739feafa9bc.png)
●数学思考
将图1中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
●拓展应用
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cee49e97546d466ba3ee630e08cdc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c750cbbbe03c2d4fb2b4ea84f659631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c252a0fe067d434a2b5aeac011b9914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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2023-03-25更新
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