19-20九年级·江西南昌·阶段练习
1 . 定义:如果三角形上有两点,其中一点为一边的中点,且这两点的连线将三角形分成周长相等的两部分,我们就称这条线段为该三角形的“等分周线”.如图1,在
中,D是
的中点,点E在
上,若
,则
为
的一条“等分周线”.
概念理解
(1)任意三角形的“等分周线”有______条,若某三角形的一条“等分周线”有一个端点是三角形的顶点,则这个三角形是______.
规律探究
(2)如图1,在
中,
为
的一条“等分周线”.若
,
,
,求
的长.(用含m,
的代数式表示).
拓展应用
(3)如图2,在四边形
中,
,
平分
,
,点E在线段
上,连接
,
,且
,
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e28d6047ece23be329d3d38d9a3f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
概念理解
(1)任意三角形的“等分周线”有______条,若某三角形的一条“等分周线”有一个端点是三角形的顶点,则这个三角形是______.
规律探究
(2)如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb980da8e86b4cfd322616dc84fc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd465973943bcd766b5275ee204bbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15fcde639611cd140a6ffcd336bc5e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
拓展应用
(3)如图2,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510634e49198fc429d942d00fa5446ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ad3e630a224303d6d3b8ad5c114ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81681f4f098511de0da54271f2b42a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6af352128fc4601065947c85c7d4a42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ee8de2d272e8a3cad423ef206cd7eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://img.xkw.com/dksih/QBM/2020/11/3/2584867635585024/2585213465640960/STEM/6e9a33fa35ce4ecb995e6ed984e9098e.png?resizew=542)
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真题
2 . 观察下列结论:
(1)如图①,在正三角形
中,点M,N是
上的点,且
,则
,
;
(2)如图②,在正方形
中,点M,N是
上的点,且
,则
,
;
(3)如图③,在正五边形
中,点M,N是
上的点,且
,则
,
;……
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/527c9392-6cd7-43e5-8694-a830fd8eca2b.png?resizew=441)
根据以上规律,在正n边形
中,对相邻的三边实施同样的操作过程,即点M,N是
上的点,且
,
与
相交于O.也会有类似的结论.你的结论是_________________ .
(1)如图①,在正三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29819c98ebd087116d5e579f4f088fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c21d6cb1025dc1990c74a563d151ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6c179debfbc0301c7beb2310cd8c4a.png)
(2)如图②,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29819c98ebd087116d5e579f4f088fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42052f4f05378f303663cb24ed092af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba613158e84d7f9b2e491652d76714d.png)
(3)如图③,在正五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29819c98ebd087116d5e579f4f088fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c8e403102e3abf521622f7d133e2ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667461bd22fdbef41f42d4c82e59b9b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/527c9392-6cd7-43e5-8694-a830fd8eca2b.png?resizew=441)
根据以上规律,在正n边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312bbdc643833d10328998f6e59d2805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5cb72419cdf0534283b7e54194ac392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c3e82ac3c3effad706fffc3c9027cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a604466a9c8d10d557b3dfc43b547065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c418285c4d2d3e9112c3adff8d17007.png)
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