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1、 三角形的内角和三角形的内角和人教新课标四年级数学下册人教新课标四年级数学下册Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/学习目标1.了解三角形的内角和
2、。2.会用平行线的性质与定义证明 三角形的内角和等于18003.学会解决求与角有关的实际问 题。4.初步培养同学们的说理能力。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教
3、育网 http:/自学指导思考：1.三角形的三个内角和是多少度？2.怎样推导证明三角形的内角和？你有 哪些方法？3.应用三角形的内角和性质能解决哪些 问题？Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose
4、Pty Ltd.绿色圃中小学教育网 http:/在一个直角三角形里住着三个内角， 平时，它们三兄弟非常团结。可是有一天 ，老二突然不高兴，发起脾气来，它指着 老大说：“你凭什么度数最大，我也要和 你一样大！”“不行啊！”老大说：“这 是不可能的，否则，我们这个家就再也围 不起来了”“为什么？” 老二很纳闷 。 同学们，你们知道其中的道理吗？内角三兄弟之争Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides
5、 for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/想一想三角形的三个内角和是多少?把三个角拼在一起试试看有什么办法可以验证呢 ?Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 C
6、lient Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/三角形的三个内角和等于180 结论对任意三角形都成立吗？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Co
7、pyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/想一想问题：有什么方法可以得到平角的度数是两直线平行，同旁内角的 和是从刚才拼角的过程你能想出 证明的办法吗?Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. C
8、opyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/A证法1： 在ABC的外部，以CA为一边， CE为另一边作1=A，E作BC的延长线CD，于是CEBA (内错角相等，两直线平行)。？ B=2？(两直线平行，同位角相等)。）1）。2又1+2+ACB=180(平角的定义) A+B+ACB=180？ ？(等量代换)E）。BCDEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client
9、 Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/ABC过C作CEBA，）E1）。于是A=1(两直线平行，内错角相等) B=2 又1+2+ACB=180(平角的定义)A+B+ACB=1802？(两直线平行，同位角相等)？ ？(等量代换)证法2：作BC的延长线CD，图形相同，画法不同， 证明也不同 。DEvaluat
10、ion only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/证法3：ABC过A作EFBC，EFB=BAE (两直线平行,内错角相等)C=CAF (两直线平行,内错角相等)BAE+CA
11、F+BAC=180B+C+BAC=180(平角的定义)(等量代换)Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/证法4：ABC过A作AEBC，EB=BAE
12、 (两直线平行,内错角相等)EAB+BAC+C=180(两直线平行,同旁内角互补)B+C+BAC=180(等量代换)Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 ht
13、tp:/在这里，为了证明的需要，在原 来的图形上添画的线叫做辅助线。在 平面几何里，辅助线通常画成虚线。 思路总结为了证明三个角的和为1800,转化 为一个平角或同旁内角互补,这种转 化思想是数学中的常用方法。 三角形内角和定理:三角形的内角和等于1800。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2
14、004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/检验一下自己吧!1、 在ABC中,A=80,B=C , 求C的度数。解：在ABC中,A+B+C=180，A=80B+C=100B=CB=C=500 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile
15、5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/2、已知三角形三个内角的度数之比 为1:3:5，求这三个内角的度数。 解：设三个内角度数分别为：x、 3x、5x列出方程 x+3x+5x=180 x=20答：三个内角度数分别为 20,60,100。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.绿色圃中小学教育网 http:/这节课你有哪些收获 ?Evaluation only.Evaluation only. Cr
