八年级数学教案：平行四边形的判定（第2课时）

这是一份八年级数学教案：平行四边形的判定（第2课时），共5页。教案主要包含了教学步骤，布置作业，板书设计，背景知识与课外阅读，随堂练习等内容，欢迎下载使用。
八年级数学教案：平行四边形的判定（第2课时）　　七、教学步骤【引入新课】 由        的定义和性质易得    且                                                        ，即“平行且相等”记为                                                        ，反过来当                                                        时，四边形                                                        必为平行四边形，这就是今天要讲的判定定理4(写出课题).                                                        【讲解新课】(1)平行四边形的判定定理4：一组对边平行且相等的四边形是平行四边形.引导学生结合图1，把已知，求证具体化.分析：因为已知       ，所以只须证出                                                                        ，为此只需连对角线                                                                                                  ，通过全等三角形来实现.                                                                                                  证明：(由学生口述)师：我们已经全面的掌握了平行四边形的判定方法，共有几个方法?哪几个?由学生归纳后用投影仪打出.             (2)平行四边形判定等知识的综合应用教师指出：平行四边形的有关知识同学们都已掌握，但如何灵活、综合、有效地用来解决有关问题是非常重要的.因此，对典型例题的分析、论证、方法技巧的探讨运用都必须引起重视.    例2 已知：                                                                                                                                                                                                                ，                                                                                                                                                                                      分别是                                                                                                                                                                                      、                                                                                                                                                                                      的中点，结合图1，求证：                                                                                                                                                                                      .                                                                                                                                                                                      分析：证明两条线段相等，从它们在图形中的位置看，可证明两个三角形全等或证明四边形                                                                                                                                                                                                                                为平行四边形(显然后者较前者简单)                                                                                                                                                                                                                                证明：(略).此例题综合运用了平行四边形的性质和判定，证题思路是：先运用平行四边形的性质得到判定另一个四边形是平行四边形的条件，再应用平行四边形的性质得出结论;题目虽不复杂，但层次有三，且利用基础知识较多，因此应使学生获得清晰的证题思路.例3 画                                                                                                                                                                                                                                                                                                                       ，使                                                                                                                                                                                                                                                                          ，                                                                                                                                                                                                                                                                          ，                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (按课本讲)【总结、扩展】1.小结平行四边形知识的运用包括三个方面：一是直接运用平行四边形的性质来解决某些问题，例如求角的度数，线段长度，证明角相等或互补，证明线段相等或倍分等;二是判定一个四边形是平行四边形，从而判定直线平行等;三是先判定一个四边形是平行四边形，然后再用四边形的性质来解决有关问题.2.思考题：       已知：如图1，在△                                                                                                                                                                                                                                      中，                                                                                                                                                                                                                                                                                                                    ，                                                                                                                                                                                                                                                                                                                    .                                                                                                                                                                                                                                                                                                                    求证：                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            八、布置作业教材P143中11、12，P144中13、14九、板书设计                                                                                                                                                                                                                                                                               十、背景知识与课外阅读美妙的莫雷定理已知：如图1，                                                                                                                                                                                                                                               和                                                                                                                                                                                                                                                                                                                                                                                                                                                  ，                                                                                                                                                                                                                                                                                                                                                                                                                                                  和                                                                                                                                                                                                                                                                                                                                                                                                                                                  ，                                                                                                                                                                                                                                                                                                                                                                                                                                                  和                                                                                                                                                                                                                                                                                                                                                                                                                                                  分别为△                                                                                                                                                                                                                                                                                                                                                                                                                                                  的                                                                                                                                                                                                                                                                                                                                                                                                                                                  、                                                                                                                                                                                                                                                                                                                                                                                                                                                  、                                                                                                                                                                                                                                                                                                                                                                                                                                                  的三等分线.                                                                                                                                                                                                                                                                                                                                                                                                                                                  求证：∠△                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            是正三角形.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            这是英国数学家富兰克·莫雷在1899年提出的，不管从已知条件和结论看，都十分对称美妙，数学家柯克特称它是初等几何最惊人的定理之一.十一、随堂练习教材P140中1、2补充：判断(1)一组对边平行，一组对边相等的四边形是平行四边形(　)(2)一组对角平行，一组对角相等的四边形是平行四边形(　)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。(3)一组对边相等，一组对角相等的四边形是平行四边形(　)“教书先生”恐怕是市井百姓最为熟悉的一种称呼，从最初的门馆、私塾到晚清的学堂，“教书先生”那一行当怎么说也算是让国人景仰甚或敬畏的一种社会职业。只是更早的“先生”概念并非源于教书，最初出现的“先生”一词也并非有传授知识那般的含义。《孟子》中的“先生何为出此言也？”；《论语》中的“有酒食，先生馔”；《国策》中的“先生坐，何至于此？”等等，均指“先生”为父兄或有学问、有德行的长辈。其实《国策》中本身就有“先生长者，有德之称”的说法。可见“先生”之原意非真正的“教师”之意，倒是与当今“先生”的称呼更接近。看来，“先生”之本源含义在于礼貌和尊称，并非具学问者的专称。称“老师”为“先生”的记载，首见于《礼记?曲礼》，有“从于先生，不越礼而与人言”，其中之“先生”意为“年长、资深之传授知识者”，与教师、老师之意基本一致。(4)一组对边平行且相等的四边形是平行四边形(　)唐宋或更早之前，针对“经学”“律学”“算学”和“书学”各科目，其相应传授者称为“博士”，这与当今“博士”含义已经相去甚远。而对那些特别讲授“武事”或讲解“经籍”者，又称“讲师”。“教授”和“助教”均原为学官称谓。前者始于宋，乃“宗学”“律学”“医学”“武学”等科目的讲授者；而后者则于西晋武帝时代即已设立了，主要协助国子、博士培养生徒。“助教”在古代不仅要作入流的学问，其教书育人的职责也十分明晰。唐代国子学、太学等所设之“助教”一席，也是当朝打眼的学官。至明清两代，只设国子监（国子学）一科的“助教”，其身价不谓显赫，也称得上朝廷要员。至此，无论是“博士”“讲师”，还是“教授”“助教”，其今日教师应具有的基本概念都具有了。