已知,在四边形
中,
分别是边
上的点,且
.
(1)为探究上述问题,小王同学先画出了其中一种特殊情况,即如图1,当
时.
小王同学探究此问题的方法是:延长
到点
,使
,连接
.
请你在图1中添加上述辅助线,并补全下面的思路.
小明的解题思路:先证明
______;再证明了
______,即可得出
之间的数量关系为
.
(2)请你借鉴小王的方法探究图2,当
时,上述结论是否依然成立,如果成立,请证明你的结论,如果不成立,请说明理由.
(3)如图3,若
分别是边
延长线上的点,其他已知条件不变,此时线段
之间的数量关系为______.(不用证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfc0c9c0106ab9ec47d0c37c7915d98b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6aef04eceb608a7a2cfc3e566f9e8b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/25/97097efe-6bef-4647-a6f6-76c68028e7d0.png?resizew=504)
(1)为探究上述问题,小王同学先画出了其中一种特殊情况,即如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21eb847a1722ed6e10e23c59d53fe7d3.png)
小王同学探究此问题的方法是:延长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab17635a999236e8d2e35017a208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc180eda08edfb6d54eb04da7741f099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
请你在图1中添加上述辅助线,并补全下面的思路.
小明的解题思路:先证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aced1cdc872e1c876f33c99cce54c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46dfacf8dd971b5a339b8fc0f9b46ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522c56ea686f93615fa6dd93e7912411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e370923be3d4b7034a5992065b5f7d7.png)
(2)请你借鉴小王的方法探究图2,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd602a957d7f6d0940f79a1121b78c6.png)
(3)如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20cb2c77ea29b6eabbc477bc3743859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bbb83c70a99a13daeb8f65512a08b04.png)
更新时间:2023-12-10 08:19:49
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【推荐2】如图,
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解答题-证明题
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名校
【推荐1】如图,△ABC中,AB=AC,点D为△ABC外一点,且∠BDC=∠BAC,AM⊥CD于M,求证:BD+DM=CM.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/7c1e84b8-e178-4796-af83-61d3b65cdd9b.png?resizew=114)
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解答题-证明题
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【推荐2】(1)如图中,已知∠MAN=120°,AC平分∠MAN.∠ABC=∠ADC=90°,则能得如下两个结论:①DC=BC; ②AD+AB=AC.请你证明结论②;
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解答题-作图题
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【推荐3】综合与实践
问题提出
如图1,在
中,
平分
,交
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,
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方法运用
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延伸探究
(3)小明发现“补短法”或“截长法”还可以帮助我们解决其他多边形中的问题.如图4,在五边形
中,
,
,
,若
,求
的度数.
问题提出
如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b903796831a684296f24e836b1fa7770.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
方法运用
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/6b318c71-5362-4ea7-922e-2cb1190256ef.jpg?resizew=530)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5fc6ead6416492c231c320a5486f86.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)以上方法叫做“补短法”.我们还可以采用“截长法”,即通过在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5f441402ee632377b6bedeb060f3d9.png)
延伸探究
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