19.1 多边形内角和 沪科版八年级数学下册教学课件

这是一份19.1 多边形内角和 沪科版八年级数学下册教学课件，共34页。
Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.知识要点1.多边形的有关概念2.多边形内角和3.多边形的外角和Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.在平面内，由若干条不在同一条直线上的线段首尾顺次相接组成的封闭图形叫做多边形.由不在同一条直线上的三条线段首尾顺次相接所组成的图形叫做三角形.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.内角：多边形相邻两边组成的角顶点：相邻两边的公共端点边：组成多边形的线段外角：在顶点处一边与另一边的延长线组成的角.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.（1）（2） 如图（1）这样，画出多边形的任何一条边所在的直线，整个多边形都在这条直线的同一侧，那么这个多边形就是凸多边形.本节我们只讨论凸多边形.ABCDEFGHEvaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.ABCDEEvaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.0123512346n-3n-2Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.已知：四边形ABCD.求证：∠A+∠B+∠C=∠D=360°.证明：如图，连接AC,所以四边形被分为两个三角形，所以四边形ABCD内角和为180°×2=360°.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.233540°720°344Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.(n-2)×180 °Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.解：如图，四边形ABCD中，∠A+ ∠C =180°.因为∠A+∠B+∠C+∠D=(4－2) ×180 °= 360 °，所以∠B＋∠D= 360°－（∠A＋∠C） = 360°－ 180° =180°.如果一个四边形的一组对角互补，那么另一组对角互补.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.BEvaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.5×180°=900°Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.五边形外角和=5个平角－五边形内角和=5×180°－(5－2)×180°=360 °Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.123465Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.解：六边形的任何一个外角加上与它相邻的内角都等于180° ，因此六边形的6个外角加上与它们相邻的内角，所得总和等于6×180°. 这个总和就是六边形的外角和加上内角和，所有外角和等于总和减去内角和，即外角和等于 6×180°-(6-2)×180°=360°.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.n边形外角和=n个平角-n边形内角和= n×180 °－(n－2) × 180°=360 °Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.每个外角的度数是每个内角的度数是Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.ADEvaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.1.判断：(1)当多边形边数增加时，它的内角和也随着增加.( )(2)当多边形边数增加时，它的外角和也随着增加.( )(3)三角形的外角和与八边形的外角和相等． ( ) Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.4.一个正多边形的内角和为720°，则这个正多边形的 每一个内角等于______．120°2.一个多边形的内角和不可能是（ ）A.1 800° B.540 ° C.720 ° D.710 °D3.一个多边形从一个顶点可引对角线3条，这个多边形 内角和等于（ ）A.360° B.540 ° C.720 ° D.900 °B Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.5.图1是我国古代建筑中的一种窗格，其中冰裂纹图案象征着坚冰出现裂纹并开始消融，形状无一定规则，代表一种自然和谐美.图2是从图1冰裂纹窗格图案中提取的由五条线段组成的图形，若∠1=115°，则∠2+∠3+∠4+∠5=______.295°Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.6.如图，小华从点A出发，沿直线前进10 m后左转24°，再沿直线前进10 m，又向左转24°，…，照这样走下去，他第一次回到出发地点A时，走的路程一共是______ m．150Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.7.已知一个多边形，它的内角和等于外角和的3倍，求这个多边形的边数.解： 设多边形的边数为n. ∵它的内角和等于 (n－2)•180°， 多边形外角和等于360°， ∴ (n－2)•180°=3× 360º. 解得 n=8. ∴这个多边形的边数为8.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.多边形的相关概念定义在平面内，由若干条不在同一条直线上的线段首尾顺次相接组成的封闭图形叫做多边形.对角线多边形中连接不相邻两个顶点的线段，叫做多边形的对角线.正多边形多边形中，如果各条边都相等，各个内角都相等，这样的多边形叫做正多边形.Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.多边形的性质内角和(n-2) × 180 °(n 是不小于3的任意整数） 外角和多边形的外角和等于360°特别注意：与边数无关.正多边形四边形具有不稳定性Evaluation only. Created with Aspose.Slides for Java 19.1. Copyright 2004-2019 Aspose Pty Ltd.