名校
1 . 在如图所示的
中,
平分
.作
的垂直平分线交
于点E,交
于点F,交
于点G,连接
.求证:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/c06a35d0-c6d2-4fa7-8a6f-55717edb8697.png?resizew=205)
(1)用尺规在答题卷上完成作图,并标上字母,保留作图痕迹,不写作法;
(2)下面是证明
的过程,请按序号在答题卷上将题中横线处补充完整.
证明:
∵
平分
,
∴ ① ,
又∵
垂直平分
,
∴
,
∴
.
∴
② ,
在
和
中,
,
,
∴
( ③ 用字母表示),
∴ ④ ,
∵
.
∴
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c818110255bdad691f61be6461a6fd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faabc484ce3666706c1beffda4bcfe2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/5/c06a35d0-c6d2-4fa7-8a6f-55717edb8697.png?resizew=205)
(1)用尺规在答题卷上完成作图,并标上字母,保留作图痕迹,不写作法;
(2)下面是证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faabc484ce3666706c1beffda4bcfe2.png)
证明:
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
∴ ① ,
又∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3484e098bdccf6c841f5a580a483104a.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f51dd2807fc3173cbc51b0aa1046f9b.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc310194575262fb45352c2fbc19868.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19697acb629aed98c7733bcffd56fd0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ed92a6827783abceb6357e9369117a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f03298b5a6c53d2577a7d7282c0aeeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9cce44e29d5da14d4e8e0e4c3e9b11.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f94fbaa8c3be3b18d5d9a04518f011.png)
∴ ④ ,
∵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314dbb3edcffa7ac3f9d4b6aef6db10a.png)
∴
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7faabc484ce3666706c1beffda4bcfe2.png)
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2023-02-27更新
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180次组卷
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2卷引用:重庆市忠县2022-2023学年八年级上学期期末数学试题