多边形及其内角和教案.pdf
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1、名师精编优秀教案多边形及其内角和本节内容选自七年级下册第七章7.3节 p84页一、教学目标1、明确表述多边形的有关概念(内角、外角、对角线、凸多边形、凹多边形,正多边形)。2、探索并说出多边形的内角和公式,能根据多边形内角和公式求多边形内角的度数和多边形的边数,进一步发展说理能力和简单的推理能力。二、教学重点1、多边形的内角和公式及其推导过程。2、利用多边形的内角和公式求多边形内角。三、教学难点1、多边形的内角和公式的推导过程四、课时安排:一课时教具准备:板书,幻灯片五、教学过程(一)引入你能从图 7.31 中找出几个由一些线段围成的图形吗?名师精编优秀教案(二)知识点我们学过三角形。三角形定
2、义: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。给出相关概念:多边形类似地,在平面内,由一些线段首尾顺次相接组成的图形叫做多边形(po1ygon)。多边形按组成它的线段的条数分成三角形、四边形、五边形三角形是最简单的多边形。如果一个多边形由n 条线段组成,那么这个多边形就叫做 n 边形。凸多边形与凹多边形如图(1)画出四边形 ABCD 的任何一条边(例如 CD)所在直线,整个四边形都在这条直线的同一侧,这样的四边形叫做凸四边形。而图(2)中的四边形 ABCD 就不是凸四边形,因为画出边CD(或 BC)所在直线,整个四边形不都在这条直线的同一侧。类似的,画出多边形的任何一条边
3、所在直线,如果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,本节只讨论凸多边形。正多边形我们知道,正方形的各个角都相等,各条边都相等。像正方形那文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A
4、9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1
5、 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文
6、档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V1
7、0A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4
8、T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F
9、4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4名师精编优秀教案样,各个角都相等,各条边都相等的多边形叫做正多边形。图 7.3 7 是正多边形的一些例子。
10、特别提醒:(1)正多边形必须两个条件同时具备,各内角都相等;各边都相等。例如:矩形各个内角都相等,它就不是正四边形。再如:菱形各边都相等,它却不是正四边形。多边形中的角我们已经知道三角形有三个内角,类似多边形相邻两边组成的角叫做它的内角。如图 7.3-3,A,B,C,D,E 是五边形 ABCDE 的五个内角,多边形的边与它的邻边的延长线组成的角叫做多边形的外角,图 7.3-4 中的 1 是五边形 ABCDE 的外角。易知n 边形有 n 个内角,有 n 个外角。文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4
11、T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F
12、4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3
13、V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4
14、Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y
15、6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9
16、Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9
17、I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4名师精编优秀教案对角线连接多边形不相邻的两个顶点的线段,叫做多边形的对角线。试着画出四边形和五边形所有的对角线。(板书)(三)探究多边形内角和从三角形内角和为180入手师:提问学生:求多边形内角和,我们是否遇到过与此相关的问题(提示学生考虑最简单的n 边形,进而回想起三角形内角和定理)用三角形内角和能求多边形内角和吗?要想利用三角形内角和定理,图中应该出现什么?这时学生会自然想到让图中出现三角形,
18、再提问:怎样做能使多边形中出现三角形,根据刚刚介绍的一些概念又想到连对角线。先看四边形,如图,画出任意一个四边形的一条对角线,都能将这个四边形分为两个三角形。这样,任意一个四边形的内角和,都等于两个三角形的内角和,即360。那五边形和六边形的内角和各是多少,n 边形呢?是否还可以通过三文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X
19、6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:C
20、N5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 H
21、L3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV
22、9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码
23、:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9
24、 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1
25、ZV9X6R8Y6F4名师精编优秀教案角形内角和为 180来推算?师生活动:首先画出多边形中从一个顶点出发的对角线,写出它的条数.(让学生说出四边形,五边形,六边形,八边形从一个顶点出发的对角线,教师在黑板上画)。再在黑板上教师和学生一起完成下表多边形边数一 个 顶点 出 发的 对 角线条数图形分 成 三 角形的个数内 角 和 的 计算规律三角形四边形五边形六边形七边形n边形归纳总结本节课重点 n 边形内角和=(n2)180。(四)习题文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6F4文档编码:CN5C9Y3V10A9 HL3M9I4Z4T1 ZV9X6R8Y6
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