如图,在△ABC中,AB=AC,AD⊥BC于点D,点E为AD上一点,连接EB,EC.求证:EB=EC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/d8db0ee4-bbf2-4240-82c0-190363046d00.png?resizew=146)
更新时间:2022-08-02 12:45:59
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解答题-证明题
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【推荐1】如图,以
的边
向外作等边
和
,连接
.
![](https://img.xkw.com/dksih/QBM/2021/9/22/2813519136448512/2813783196753920/STEM/e4a244f4-207b-4ac2-a0fd-abb446217bf5.png)
(1)线段
和
有什么数量关系?试证明你的结论.
(2)求出
的度数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692c58a2af64d705cd4a988ed2bfbc3d.png)
![](https://img.xkw.com/dksih/QBM/2021/9/22/2813519136448512/2813783196753920/STEM/e4a244f4-207b-4ac2-a0fd-abb446217bf5.png)
(1)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(2)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35cfb01d9e4729e9b41eb33feb5b8c6.png)
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【推荐2】如图,
,且
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/2a0d6773-3157-4f14-ac07-7fdc9179eef8.png?resizew=272)
(1)如图1,连接
、
,求证:
;
(2)如图2,求证
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6d5f85aedd049d78ffd0f5ad60fe9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a2ab6940dca62be1f3b2b5f8531990.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/20/2a0d6773-3157-4f14-ac07-7fdc9179eef8.png?resizew=272)
(1)如图1,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c78e28e81eab02564ba523cf0e5ae2a.png)
(2)如图2,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a5d84be7704cbb1c2d1d4bc3fb8bf2.png)
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解答题-证明题
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【推荐1】如图,在△ABC中,AB=CB,BD平分∠ABC交AC于点D,点E在线段BD上,点F在BD的延长线上,且DE=DF,顺次连接A、E、C、F.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/29/bc063c25-3d66-46e4-bf10-ca4e8873fc51.png?resizew=132)
(1)求证:四边形AECF是菱形.
(2)若EF=2,AC=4,直接写出四边形AECF的周长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/29/bc063c25-3d66-46e4-bf10-ca4e8873fc51.png?resizew=132)
(1)求证:四边形AECF是菱形.
(2)若EF=2,AC=4,直接写出四边形AECF的周长.
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【推荐2】如图,AD∥BC,∠BAC=70°,DE⊥AC于点E,∠D=20°.
(1)求∠B的度数,并判断△ABC的形状;
(2)若延长线段DE恰好过点B,试说明DB是∠ABC的平分线.
(1)求∠B的度数,并判断△ABC的形状;
(2)若延长线段DE恰好过点B,试说明DB是∠ABC的平分线.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/4db7cf8f-932a-45af-91ea-244f632d342b.png?resizew=187)
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