如图,在四边形
中,
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e53497af8899cb299d762f1a4f46a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bd8869f34219e7fbe5a9b8842667c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
更新时间:2024-04-10 23:59:11
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解答题-证明题
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【推荐1】如图,点
,
,
,
在同一条直线上,已知
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439fbb8974a5f907205d26b47b420bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c436f108fd4921dae15ecff19270237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a510a3eb906b3ef0760b0d1723d11ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542608b4938fad4da1cd55788887e043.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/684518d6-3d12-4e5f-a994-4a2509f098c7.png?resizew=190)
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【推荐2】学习了平行线后,某同学通过折纸想出了过点P画直线A
的平行线的方法,折纸过程如下:①−④
(1)通过上述的折纸过程,图②的折痕
与直线
的位置关系是 ;
如图④,
,则
与
的位置关系为 ,
依据是 .
(2)保持(1)中
与
的位置关系不变,将直线
绕点P旋转至如图⑤,当
时,则
与
平行吗?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/15/72bfb843-9da8-4ad1-b251-b14adfc1df56.png?resizew=507)
(1)通过上述的折纸过程,图②的折痕
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
如图④,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e5bd1f7d62405cc1890de21ec25349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83873a9d782f2588c5eedbfe73f9bc2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
依据是 .
(2)保持(1)中
![](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/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812c95bb449dad47e37a5464cabee49c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/15/99a6c415-ffa1-4ca2-8600-5825ec752e5c.png?resizew=126)
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【推荐1】探究题:
(1)已知:三角形
,求证:
;小明同学经过认真思考,他过点C作
,利用添加辅助线的方法成功解决了这个问题.你能说出小明是怎么解决这个问题的吗?写出论证过程.
![](https://img.xkw.com/dksih/QBM/2021/9/22/2813632951066624/2813759792431104/STEM/7ac0d1c3-4912-44dd-8a32-674b627db9b5.png)
(2)利用以上结论或方法,解决如下问题:已知:六边形
,满足
,求证:
.
(1)已知:三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e672231ec121e6fe99f3dc5f5e642493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e40e939cffbcc5d184ee668be120b3.png)
![](https://img.xkw.com/dksih/QBM/2021/9/22/2813632951066624/2813759792431104/STEM/7ac0d1c3-4912-44dd-8a32-674b627db9b5.png)
(2)利用以上结论或方法,解决如下问题:已知:六边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803e40715fac89ab9c03ca19e7b49ec8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c97c0332c0510792375004aef6e0ea.png)
![](https://img.xkw.com/dksih/QBM/2021/9/22/2813632951066624/2813759792431104/STEM/e95572a2-4311-4b88-b97f-1b013d8e628c.png)
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【推荐2】如图,已知DE//BC,BE平分∠ABC,∠C=55°,∠ABC=70°,求∠BED与∠BEC的度数.
![](https://img.xkw.com/dksih/QBM/2019/6/10/2222525430833152/2223377333231616/STEM/6b6f167588954e16aee487762da4be2d.png?resizew=264)
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