人教版八年级上册13.3.2 等边三角形教案

这是一份人教版八年级上册13.3.2 等边三角形教案，共4页。
含有30度角的直角三角形项目设计内容备 注课时第1课时课 型新课教具三角板、刻度尺、圆规 教学目标知识与能力掌握含30度角的直角三角形的性质与应用 过程与方法通过探究含30度角的直角三角形的性质，增强学生对特殊直角三角形的认识 态度与情感培养学生用发展变化的思想看问题的价值观 重点 含30度的直角三角形的性质 难点含30度的直角三角形的性质的推导  教学手段方法动手操作，讲练结合 教学过程教师活动学生活动说明或设计意图情境导入   复习巩固等边三角形的性质:   三边相等 ，三个角都是60，“三线合一”，三条对称轴. 等边三角形的判定: 定义:有三边相等的三角形是等边三角形.定理1:有一个角是60的等腰三角形是等边三角形.定理2:三个角都相等的三角形是等边三角形.    学生回顾口答 新知教学 操作探究1.量一量含30°角的直角三角尺的最短直角边与斜边你有什么发现？ 2.用两个全等的含30°角的直角三角尺你能拼出一个等边三角形吗？说说你的理由．3. 在直角三角形中，30°角所对的直角边与斜边有怎样的大小关系？ 在直角三角形中，如果有一个锐角等于300，那么它所对的直角边等于斜边的一半。已知：如图，在Rt△ABC中，∠C=90°， ∠BAC=30° 求证：BC= AB证明：延长BC至D，使CD=BC，连结AD.在△ABC与△ADC中BC＝DC ∠ACB=∠ACDAC=AC∴ △ABC≌△ADC（SAS）∴AB=AD∴ △ABD 是等边三角形∴BC＝DC＝BD=AB            含30 °直角三角形性质：   在直角三角形中，如果一个锐角等于30°，那么它所对的直角边等于斜边的一半。几何语言：∵在Rt△ABC中，∠C=90°，∠A= 30° ∴ BC=AB                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 学生探究另一种证法   在BA上截取BE=BC，连接EC   ∵  ∠B= 60°     BE=BC ∴ △BCE是等边三角形，BE=EC ∴ ∠BEC= 60° ∵ ∠A= 30°  ∴ ∠ECA= 30° ∴ AE=EC， ∴ AB=AE+BE=2BC.                        从实验到证明，从理论上肯定正确性          让学生通过多种方法得到斜边与短直角边的关系，加深印象                              课堂练习1）直角三角形中30°角所对的直角边等于另一直角边的一半．
2）三角形中30°角所对的边等于最长边的一半。
3）直角三角形中最小的直角边是斜边的一半。
4）直角三角形的斜边是30°角所对直角边的2倍．1、如图，在Rt△ABC中∠C=900 ,∠B=2 ∠A，AB=6cm，则BC=________.2、如图， Rt△ABC中，∠A= 30°，AB+BC=12cm，则AB= _______.3、如图， Rt△ABC中， ∠A= 30°，BD平分∠ABC，      且BD=16cm，则AC=                  .     学生独立完成 课堂小结    含30 °直角三角形性质：   在直角三角形中，如果一个锐角等于30°，那么它所对的直角边等于斜边的一半。几何语言：∵在Rt△ABC中，∠C=90°，∠A= 30° ∴ BC=AB  课外作业 如图在△ＡＢＣ中，ＡＢ＝ＡＣ，∠BAC＝120°,ＡＣ的垂直平分线ＥＦ交ＡＣ于点Ｅ，交ＢＣ于点Ｆ．求证：ＢＦ＝２ＣＦ．     板书设计                    含30度角的直角三角形1、复习巩固2、探究新知3、课堂练习4、课堂小结5布置作业   课后反思