如图,已知在▱ABCD中,E、F是对角线AC上的两点,且DF∥BE.求证:四边形BEDF是平行四边形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/25/1927dfee-a962-400e-8bac-52a52768e8b3.jpg?resizew=173)
更新时间:2020-07-25 07:27:54
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解答题-证明题
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【推荐1】如图,在
中,G是BC的中点,点F在CD上,FG的延长线与AB的延长线交于点E,连接BF,CE.
![](https://img.xkw.com/dksih/QBM/2022/4/17/2965982625226752/2987140466966528/STEM/28d301fe-2322-4d32-a984-5e122e4285e1.png?resizew=193)
(1)求证:四边形CEBF是平行四边形;
(2)若
,
,求EF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://img.xkw.com/dksih/QBM/2022/4/17/2965982625226752/2987140466966528/STEM/28d301fe-2322-4d32-a984-5e122e4285e1.png?resizew=193)
(1)求证:四边形CEBF是平行四边形;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d888e40f68fe8a24d5dc9c749024808.png)
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解答题-证明题
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【推荐2】已知平行四边形
,E为
边上的中点.
,求证:
平分
;
(2)若F为
边上一点,连接
;
①如图2,若
,
,求
;
②如图3,若
,请你写出线段
之间的数量关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7696b2eef050ee102ef53441a8f56bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b69923f7d2733e929c02575e7eed623.png)
(2)若F为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4dbe05cb8855c8be6192eec0b9d303.png)
①如图2,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a7f5ecd3b2166cfc3459eba68b05f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8b5fa3297799d583fde6d9c7b8f26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef318d955867777f6af6090084c188d.png)
②如图3,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ea5fc2cd827dd23ffe46714677da3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b77b9ddc2305b41a176688b05e69b7a3.png)
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解答题-证明题
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【推荐1】如图,在四边形
中,
,
,点
,
分别是
,
上的点,且
,求证:四边形
是平行四边形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92034dd2bb9480b18709d01153467f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dceb5cc71fc50f20649f6b9535fd914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d527b7de54224cc1698843a59a19a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2023/5/28/3247613960536064/3259946891780096/STEM/409ec80d79c1430c8c628a748d75349e.png?resizew=176)
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【推荐2】如图,矩形
的对角线
相交于点O,延长
到E,使
,连接
.
是平行四边形:
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fa1aa5a7a5bb172ed4603f17c8b2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c9218263b2715b3781862932ddc81c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8384da01b6e050cf11ea979fe6671e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
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