【问题情境】
利用角平分线构造全等三角形是常用的方法,如图1,
平分
.点
为
上一点,过点A作
,垂足为C,延长
交
于点B,可根据______证明
,则
,
(即点C为
的中点).
【类比解答】
如图2,在
中,
平分
,
于E,若
,
,通过上述构造全等的办法,可求得
______.
【拓展延伸】
(1)如图3,
中,
,
,
平分
,
,垂足E在
的延长线上,试探究
和
的数量关系,并证明你的结论.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/e6116658-178c-4e35-bcb4-8f205f15c939.png?resizew=440)
(2)如图4,
中,
,
,点D在线段
上,
,
,垂足为
,
与
相交于点F.线段
与
的数量关系为______.(直接写出)
利用角平分线构造全等三角形是常用的方法,如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101a7b5c8a4aed0de2af363792e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a2fe360dbaf805c6b8bff7b07c1dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075bc6df108c9c2b3b5ac46bca7c8d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ae5640206c24e99d0c2584e632a46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129f2a8a3a38ec4119d5e1016dd04f1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
【类比解答】
如图2,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79fff206344e255d7aa364e78e35152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2507d3a2e1344315f80237c91e5c4c34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e910dce5a57ff0d917e0b4dd620214.png)
【拓展延伸】
(1)如图3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b937442ad4cc480adc11bb143559454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/e6116658-178c-4e35-bcb4-8f205f15c939.png?resizew=440)
(2)如图4,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65dfd32cc6ff4d10f7992d84915043f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c182a9d9fd0a7023b710cd671d9468e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faee0268e5ede6318697e5a8509dd6f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/a1662243-d315-4164-882f-298f7a785174.png?resizew=153)
更新时间:2024-01-29 18:06:53
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【推荐2】在
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
小芳同学解题过程如下:
解:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c56afd59592dbb194c87cdd725b7dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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名校
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