八年级数学教案计：平行四边形的判定（第1课时）

这是一份八年级数学教案计：平行四边形的判定（第1课时），共7页。教案主要包含了素质教育目标，学法引导，重点·难点·疑点及解决办法，课时安排，教具学具准备，师生互动活动设计，教学步骤，布置作业等内容，欢迎下载使用。
八年级数学教案计：平行四边形的判定（第1课时）　　(第一课时)一、素质教育目标(一)知识教学点1.掌握平行四边形的判定定理1、2、3、4，并能与性质定理、定义综合应用.2.使学生理解判定定理与性质定理的区别与联系.3.会根据简单的条件画出平行四边形，并说明画图的依据是哪几个定理.(二)能力训练点1.通过“探索式试明法”开拓学生思路，发展学生思维能力.2.通过教学，使学生逐步学会分别从题设或结论出发寻求论证思路的分析方法，进一步提高学生分析问题，解决问题的能力.(三)德育渗透点通过一题多解激发学生的学习兴趣.(四)美育渗透点通过学习，体会几何证明的方法美.二、学法引导构造逆命题，分析探索证明，启发讲解.三、重点·难点·疑点及解决办法1.教学重点：平行四边形的判定定理1、2、3的应用.2.教学难点：综合应用判定定理和性质定理.3.疑点及解决办法：在综合应用判定定理及性质定理时，在什么条件下用判定定理，在什么条件下用性质定理(强调在求证平行四边形时用判定定理，在已知平行四边形时用性质定理).四、课时安排2课时五、教具学具准备投影仪，投影胶片，常用画图工具六、师生互动活动设计复习引入，构造逆命题，画图分析，讨论证法，巩固应用.七、教学步骤【复习提问】1.平行四边形有什么性质?学生回答教师板书     2.将以上性质定理分别用命题的形式叙述出来.【引入新课】用投影仪打出上述命题的逆命题.上述第一个逆命题显然是正确的，因为它就是平行四边形的定义，所以它也是我们判定一个四边形是否为平行四边形的基本方法(定义法).那么其它逆命题是否正确呢?如果正确就可得到另外的判定方法(写出命题).【讲解新课】1.平行四边形的判定我们知道，平行四边形的对角相等，反过来对角相等的四边形是平行四边形吗?如图1，在四边形       中，如果                                              ，                                                                                                  ，那么                                                                                                  .                                                                                                                                                                                                                                                                                                                                                                                          ∴                                                                                                                                                                                      .                                                                                                                                                                                      同理                                                                                                                                                                                                                                .                                                                                                                                                                                                                                ∴四边形                                                                                                                                                                                                                                                                          是平行四边形，因此得到：                                                                                                                                                                                                                                                                          平行四边形判定定理1：两组对角分别相等的四边形是平行四边形.类似地，我们还会想到，两组对边相等的四边形是平行四边形吗?如图1，如果                                                                                                                 ，                                                                                                                                                                                                                                                                                                                    ，连结                                                                                                                                                                                                                                                                                                                    ，则△                                                                                                                                                                                                                                                                                                                    ≌△                                                                                                                                                                                                                                                                                                                    得到                                                                                                                                                                                                                                                                                                                    ，                                                                                                                                                                                                                                                                                                                    ，那么                                                                                                                                                                                                                                                                                                                    ，                                                                                                                                                                                                                                                                                                                    ，则四边形                                                                                                                                                                                                                                                                                                                    是平行四边形.                                                                                                                                                                                                                                                                                                                    由此得到：平行四边形判定定理2：两组对边分别相等的四边形是平行四边形.(判定定理1、2的证明采用了探索式的证明方法，即根据题设和已有知识，经过推理得出结论，然后总结成定理).我们再来证明下面定理平行四边形判定定理3：对角线互相平分的四边形是平行四边形.(该定理采用规范证法，如图1由学生自己证明，教师可引导学生用前面三种依据分别证明，借以巩固所学知识)                                                                                                                                                                                                                       2.判定定理与性质定理的区别与联系判定定理1、2、3分别是相应性质定理的逆定理，彼此之间分别为互逆定理，在使用时不得混淆.         例1　已知：                                                                                                                                                                                                                                                                                                                          是                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                对角线                                                                                                                                                                                                                                                                                                                                                                                                        上两点，并且                                                                                                                                                                                                                                                                                                                                                                                                        ，如右图.                                                                                                                                                                                                                                                                                                                                                                                                        求证：四边形                                                                                                                                                                                                                                                                                                                                                                                                                                                  是平行四边形.                                                                                                                                                                                                                                                                                                                                                                                                                                                  分析：因为四边形                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            是平行四边形，所以对边平行且相等，由已知易证出两组三角形全等，用定义或判定定理1、2都可以，还可以连结                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            交                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            于                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            利用判定定理3简单.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            证明：(由学生用各种方法证明，可以巩固所学过的知识和作辅助线的方法，并比较各种证法的优劣，从而获得证题的技巧).【总结、扩展】1.小结：(投影打出)(1)本堂课所讲的判定定理有                                                                                                                                                                                                                                                                                                                                                                                                                                                       (2)在今后解决平行四边形问题时要尽可能地运用平行四边形的相应定理，不要总是依赖于全等三角形，否则不利于掌握新的知识.2.思考题教材P144B.3八、布置作业教材P142中7;P143中8、9、10九、板书设计                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               十、随堂练习教材P138中1、2补充这个工作可让学生分组负责收集整理,登在小黑板上,每周一换。要求学生抽空抄录并且阅读成诵。其目的在于扩大学生的知识面,引导学生关注社会,热爱生活,所以内容要尽量广泛一些,可以分为人生、价值、理想、学习、成长、责任、友谊、爱心、探索、环保等多方面。如此下去,除假期外,一年便可以积累40多则材料。如果学生的脑海里有了众多的鲜活生动的材料,写起文章来还用乱翻参考书吗?单靠“死”记还不行,还得“活”用,姑且称之为“先死后活”吧。让学生把一周看到或听到的新鲜事记下来,摒弃那些假话套话空话,写出自己的真情实感,篇幅可长可短,并要求运用积累的成语、名言警句等,定期检查点评,选择优秀篇目在班里朗读或展出。这样,即巩固了所学的材料,又锻炼了学生的写作能力,同时还培养了学生的观察能力、思维能力等等,达到“一石多鸟”的效果。1.下列给出了四边形                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          中                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          、其实,任何一门学科都离不开死记硬背,关键是记忆有技巧,“死记”之后会“活用”。不记住那些基础知识,怎么会向高层次进军?尤其是语文学科涉猎的范围很广,要真正提高学生的写作水平,单靠分析文章的写作技巧是远远不够的,必须从基础知识抓起,每天挤一点时间让学生“死记”名篇佳句、名言警句,以及丰富的词语、新颖的材料等。这样,就会在有限的时间、空间里给学生的脑海里注入无限的内容。日积月累,积少成多,从而收到水滴石穿,绳锯木断的功效。