如图,点D,E在线段
上,
,求证:
为等边三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9ad383e15899d1d08be6db610c3f2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
更新时间:2023-04-11 12:24:52
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解答题-证明题
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【推荐2】推理填空
已知:如图,
,点C、F在
上,
,
,求证:
.
证明:∵
,
∴
( ).
∵
.
∴
( ).
即:
.
在
和
中.
.
∴
( ),
∴
,
∴ ( ).
已知:如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67df12a5958f9dae3a59e5fe68face07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717ca619f3a9d1686e14280d1bbc2b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dab0c0c0f988903f228a6510208420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd81adb13f5a7550b0f94f770900a613.png)
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67df12a5958f9dae3a59e5fe68face07.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3dd1bbc94da71c226094bd624c1b46.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717ca619f3a9d1686e14280d1bbc2b53.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf39fd2cdfed8fd16ff200b1b17d92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49513c03f7fd8fa02ab37fec019a10f.png)
即:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac80c8292324adda67673aeb6619f51b.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5f4d6bfc07e09e22b98f2ad80d034e6.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00635dfbeb1f612c5dde8e2d1b645a09.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c4d9803e618d1998d1717000cea1b4.png)
∴ ( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/26/e3b2404a-a45e-47ec-9c00-807e220de3ef.jpg?resizew=127)
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【推荐1】若一个三角形的三边长分别为a,b,c,且满足
.试判断该三角形的形状,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e93c7b73a241af038ff0319b1e89a0.png)
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【推荐2】如果
,
,
是三角形
的三边,并且满足等式
,试确定三角形
的形状
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cd417d54a0e0dee5bfb94bf1f5971f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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