《菱形》课件1人教版八年级.ppt

Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 矩形与菱形 矩形 菱形 定义 有一角是直角的平行 四边形叫做矩形. 有一组邻边相等的平行四 边形叫做菱形. 具有平行四边形的一切性质 性质 边 角 对角线 四个角都是直角 相等 互相垂直且平分每一组对角 判定 有一角是直角的平行四边形 对角线相等的平行四边形 三个角都是直角的四边形 四条边都相等 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. u根据菱形的定义,可得菱形的 第一个判定的方法 四边形ABCD是平行四边形且AB=AD 四边形ABCD是菱形 数学语言： 有一组邻边相等的平行四边形叫做菱形 还有其他么方法吗? Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 探究一 用一长一短两根细木条,在它们的中点 处固定一个小钉,做成一个可以转动的十字, 四周围上一根橡皮筋,做成一个四边形.转动 木条,这个四边形什么时候变成菱形? 猜想：猜想： 对角线互相垂直的 平行四边形是菱形. Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 命题：对角线互相垂直的平行四边形是菱形. 已知：在 中，AC BDABCD ABCD求证： 是菱形 A B C D O 证明： 四边形ABCD是平行四边形 OA=OC 又ACBD; BA=BC ABCD是菱形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 判定方法2： u对角线互相垂直的平行四边形是菱形 ACBD 在ABCD中，ACBD ABCD是菱形 A B C D 菱形ABCD A BC D ABCD 数学语言 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 先画两条等长的线段AB、AD，然后分别以 B、D为圆心，AB为半径画弧，得到两弧的交点 C，连接BC、CD，就得到了一个四边形，猜一 猜，这是什么四边形？说出你的理由 猜想：有四条边相等的四边形是菱形。 A B C D O 探究二 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 命题：有四条边相等的四边形是菱形。 已知：在四边形ABCD中,AB=BC=CD=DA. 求证：四边形ABCD是菱形 D A B C 证明： AB=CD,AD=BC 四边形ABCD是平行四边形 又AB=AD, 四边形ABCD是菱形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. u四条边都相等的四边形是菱形. AB=BC=CD=DA A B C D 菱形ABCD 在四边形ABCD中 AB=BC=CD=DA 四边形ABCD是菱形 四边形ABCD A B C D 判定方法3： 数学语言 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 菱形常用的判定方法： 有一组邻边相等的平行四边形叫做菱形 对角线互相垂直的平行四边形是菱形 有四条边相等的四边形是菱形。 +邻边相等 = +对角线线互相垂直= 四条边相等+ = Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 文字语言图形语言符号语言 判定 法一 判定 法二 对角线互相垂直 的平行四边形是 菱形 判定 法三 四边相等的四边 形是菱形 菱形的判定： A B C D AB=BC=CD=DA 四边形ABCD是菱形 在ABCD中 ACBD 四边形ABCD是菱形 在ABCD中 AB=AD 四边形ABCD是菱形 A BC D O A B C D 一组邻边相 等的平行四 边形是菱形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1、老师说下列三个图形都是菱形,你相信吗? 5 5 3 4 3 4 5 5 5 5 有一组邻边 相等的平行四 边形叫做菱形 对角线互相 垂直的平行四 边形是菱形 有四条边相等的 四边形是菱形。 3 3 44 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2、判断下列说法是否正确？为什么？ (1)对角线互相垂直的四边形是菱形； （ ） (2)对角线互相垂直平分的四边形是菱形；（ ） (3)对角线互相垂直,且有一组邻边相等 的四边形是菱形； （ ） (4)两条邻边相等，且一条对角线平分一 组对角的四边形是菱形 （ ） A D B C A B C D Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 3、ABCD的对角线AC与BD相交于点O， （1）若AB=AD，则ABCD是 形； （2）若AC=BD，则ABCD是 形； （3）若ABC是直角，则ABCD是 形； （4）若BAO=DAO，则ABCD是 形。 A B C D O 矩 菱 矩 菱 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. （1）.下列命题中正确的是（ ） A.一组邻边相等的四边形是菱形 B.三条边相等的四边形是菱形 C.四条边相等的四边形是菱形 D.四个角相等的四边形是菱形 C （2）.对角线互相垂直且平分的四边形是（ ） A.矩形 B.一般的平行四边形 C.菱形 D.以上都不对 C （3）.下列条件中，不能判定四边形ABCD为菱形的是（ ） A.ACBD,AC与BD互相平分 B.AB=BC=CD=DA C.AB=BC,AD=CD,且ACBD D.AB=CD,AD=BC,ACBD C 4、选择： Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 24菱形 5、一边长为5cm平行四边形的两条对角 线的长分别为6cm和8cm，则这个平行四边 形为 ，其面积为 。 A B C D E F 6、如图在菱形ABCD中,CEAB,CFAD. 则CE CF，BE DF。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 7、如图， ABCD的两条对角线AC、BD相交于 点O，AB=5，AC=8，DB=6 求证:四边形ABCD是菱形. A B C D O 四边形ABCD是菱形. OA=OC=4 OB=OD=3 证明: 又AB=5 ACBD AOB=90 又 四边形ABCD是平行四边形 四边形ABCD是平行四边形 AB2=AO2+BO2 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 8、已知：如图，AD平分BAC，DEAC 交AB于E，DFAB交AC于F 求证：四边形AEDF是菱形 AEDF是菱形 证明：DEAC DFAB 四边形AEDF是平行四边形 DEAC 2=3 AD是ABC的角平分线 1=2 AE=DE 1=3 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 9、如图，顺次连接矩形ABCD各边中点，得到 四边形EFGH，求证：四边形EFGH是菱形。 H G F E D C B A 证明：连接AC、BD 四边形ABCD是矩形 AC=BD 点E、F、G、H为各边中点 EF=FG=GH=HE 四边形EFGH是菱形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 10、已知：如图, ABCD的对角线AC的 垂直平分线与边AD，BC分别交于E，F 求证：四边形AFCE是菱形 A B F C D E O EF垂直平分AC AO=CO, AOE=90 FOC=AOE=90 四边形ABCD是平行四边形 ADBC AEFC AEO=CFO AEOCFO 证明： OE=OF 又AO=CO 四边形AFCE是平 行四边形 又EFAC 四边形AFCE是菱形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. AD CB E F 把两张等宽的纸条交叉重叠在一起，你能判断 重叠部分ABCD的形状吗？ 思考: 请你动脑筋 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 如图，ADBC，BD垂直平分AC， 四边形ABCD一定是菱形吗？若是， 请说明理由。 C D B A O u思考题 : ) 1 2 ( 提示: AODCOB（角边角） AD=BC Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 四条边都相等 菱形 一组邻边相等 对角线互相垂直 对角线互相平分 一组对边平行且相等 二组对边平行或相等 四边形 平行四边形 两组对角相等 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1、如图，已知在ABCD中， AD=2AB，E、F在直线线AB上，且 AE=AB=BF，说说明CEDF. AB F N D M E C Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. A BC D O E 2.如图，矩形ABCD的对角线相交于点 O，DEAC,CE BD. 求证：四边形OCED是菱形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 3.如图，ABC中，AC的垂直平分线MN交 AB于点D，交AC于点O，CEAB交MN于 点E，连接AE、CD. 求证：四边形ADCE是菱形 B C A D O E M N Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 4、如图，RtABC中，ACB=900， BAC=600，DE垂直平分BC，垂足为D， 交AB于E，又点F在DE的延长线上，且 AF=CE，求证：四边形ACEF是菱形。 A B C D E F Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 5、如图:将菱形ABCD沿AC方向平移至A1B1C1D1,