【教材呈现】下图是华师版八年级下册数学教材第83页和84页的部分内容.
平行四边形的判定定理2 一组对边平行且相等的四边形是平行四边形.
我们可以用演绎推理证明这一结论.
已知:如图,在四边形
中,AB
CD且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/24/78567023-2a5b-428f-8390-3380e8b12640.png?resizew=207)
求证:四边形
是平行四边形.
证明:连接
.
(1)请根据教材提示,结合图,写出完整的证明过程.
(2)【知识应用】如图①,在
中,延长
到点
,使
,连接
、
.求证:四边形
是平行四边形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/24/6253b314-ee93-4487-b777-356c4fce1d5c.png?resizew=244)
(3)【拓展提升】在【知识应用】的条件下,若四边形
的面积为7,直接写出四边形
的面积.
平行四边形的判定定理2 一组对边平行且相等的四边形是平行四边形.
我们可以用演绎推理证明这一结论.
已知:如图,在四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c220eadc312101e2fb89dfe920f7b30d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/24/78567023-2a5b-428f-8390-3380e8b12640.png?resizew=207)
求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
证明:连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)请根据教材提示,结合图,写出完整的证明过程.
(2)【知识应用】如图①,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3214c853ea2268ef6c434fb28f0298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/24/6253b314-ee93-4487-b777-356c4fce1d5c.png?resizew=244)
(3)【拓展提升】在【知识应用】的条件下,若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
21-22八年级下·吉林长春·阶段练习 查看更多[6]
吉林省长春汽车经济技术开发区2021-2022学年八年级下学期线上教学质量检测数学试题吉林省长春市长春汽车经济技术开发区2021-2022学年八年级下学期期末数学试题(已下线)专题9.9 平行四边形(基础篇)(专项练习)-2022-2023学年八年级数学下册基础知识专项讲练(苏科版)(已下线)数学(江苏南京B卷)-学易金卷:2022-2023学年八年级下学期期中考前必刷卷(已下线)专题 4.32 平行四边形(全章复习与巩固)(知识讲解)-2022-2023学年八年级数学下册基础知识专项讲练(浙教版)(已下线)专题4.4 平行四边形的判定定理(知识要点+专项练习)-2022-2023学年八年级数学下册同步精品课堂(浙教版)
更新时间:2022-08-19 10:23:02
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【推荐2】如图,已知在
中,
、
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分别是
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的中点,连接
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是平行四边形;
(2)若
=
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=
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的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2443a94bed3d2b1f95c04ebd61ac134a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a0387fc1258f31e44a10068c0ccfd0.png)
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