【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,在矩形ABCD中,连接对角线AC、BD,将△ABC沿BC方向平移,使点B移到点C,得到△DCE.求证:△ACD≌△EDC.
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【推荐1】如图,中
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【推荐2】课本再现:
(1)如图1,在
中,D、E分别是
、
的中点,则线段
与边
的数量关系是 ,位置关系是 ;
拓展应用:
(2)如图2在
中,连接
延长至点E.连接
并延长至点F,使得
,连接
.求证:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/12/7f0df8a6-1e5e-4f4d-be69-df7cb5a6c519.png?resizew=292)
(1)如图1,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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拓展应用:
(2)如图2在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9a9618018d717926540d1452f76e44.png)
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【推荐1】如图,矩形
中,点
是
中点,线段
的延长线与
的延长线交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/ee3c6514-4f0d-431e-9142-827f0d569043.png?resizew=160)
(1)求证:
;
(2)连接
,
,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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/6/ee3c6514-4f0d-431e-9142-827f0d569043.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749f286c450a2bbc928ae04388287b8f.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
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【推荐2】如图,平行四边形
的对角线
、
交于点
,
、
是线段
上的两点,并且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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【推荐3】下面是小东设计的“作平行四边形ABCD,使∠B=45°,AB=2cm,BC=3cm”的作图过程.作法:如图,①画∠B=45°;②在∠B的两边上分别截取BA=2cm,BC=3cm.③以点A为圆心,BC长为半径画弧,以点C为圆心,AB长为半径画弧,两弧相交于点D;则四边形ABCD为所求的平行四边形.根据小东设计的作图过程:
![](https://img.xkw.com/dksih/QBM/2022/2/22/2921870611734528/2922431271550976/STEM/4fd4f03e59cd497491cb40ad99b08243.png?resizew=189)
(1)使用直尺和圆规,补全图形;(保留作图痕迹)
(2)完成下面的证明.
证明:∵AB= ,CB= ,
∴四边形ABCD为所求的平行四边形( )(填推理的依据).
![](https://img.xkw.com/dksih/QBM/2022/2/22/2921870611734528/2922431271550976/STEM/4fd4f03e59cd497491cb40ad99b08243.png?resizew=189)
(1)使用直尺和圆规,补全图形;(保留作图痕迹)
(2)完成下面的证明.
证明:∵AB= ,CB= ,
∴四边形ABCD为所求的平行四边形( )(填推理的依据).
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