尺规作图并完成证明.
如图,点
,
在
外,连接
、
、
,且
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/d453d866-544d-4656-b580-6842cd8f21c4.png?resizew=107)
(1)用尺规作图完成以下基本作图:作
的平分线
交
于点
,连接
(保留作图痕迹,不写做法,不下结论);
(2)根据(1)中的作图,求证:
;
请完善下面的证明过程.
证明:∵
平分![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
∴
___________
∵![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6095bae4840bfa80f2468f94b2002d7b.png)
∴
___________
∴![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95165e75fd7ce2d553ae30298a453b22.png)
∴___________
在
和
中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19794a725a058b3d9f04b6aaefee27e2.png)
∴
(___________)
∴
如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6095bae4840bfa80f2468f94b2002d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd44e7b89f25f7242e009653f268d72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01476dfb5970e27f54f742c27b9515f9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/d453d866-544d-4656-b580-6842cd8f21c4.png?resizew=107)
(1)用尺规作图完成以下基本作图:作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(2)根据(1)中的作图,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42218a68301d770accaaefb96b19f8a.png)
请完善下面的证明过程.
证明:∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7cecd2d5b7eac66bfd39a1d0b555b3.png)
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6095bae4840bfa80f2468f94b2002d7b.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7cecd2d5b7eac66bfd39a1d0b555b3.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95165e75fd7ce2d553ae30298a453b22.png)
∴___________
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2036191be2322003aaee6bb411868327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19794a725a058b3d9f04b6aaefee27e2.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b5ab0ba08b186c8045b6c7a31bb2de.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42218a68301d770accaaefb96b19f8a.png)
更新时间:2022-11-01 22:32:48
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【推荐1】已知在
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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