2022年27.2.3相似三角形的周长与面积[新人教版九年级下] .pdf

名师精编优秀教案第二十七章相似2723 相似三角形的周长与面积教学目标1 经历探索相似三角形性质的过程，并在探究过程中发展学生积极的情感、态度、价值观，体验解决问题策略的多样性。2理解并掌握相似三角形周长的比等于相似比、面积比等于相似比的平方，并能用来解决简单的问题。3探索相似多边形周长的比等于相似比、面积比等于相似比的平方，体验化归思想。教学重点与难点重点：理解并掌握相似三角形周长的比等于相似比、面积比等于相似比的平方。难点：探索相似多边形周长的比等于相似比、面积比等于相似比的平方。教学设计教学过程设计意图说明新课引入：1回顾相似三角形的概念及判定方法。2复习相似多边形的定义及相似多边形对应边、对应角的性质。以旧引新，帮助学生建立新旧知识间的联系。提出问题：如果两个三角形相似，它们的周长之间什么关系？两个相似多边形呢？（学生小组讨论）?ABC?A1B1C1，相似比为k111111ABBCCAkA BB CC AAB=kA1B1,BC=kB1C1,CA=kC1A1111111111111111111ABBCCAkA BkB CkC AkA BB CC AA BB CC A相似三角形周长的比等于相似比相似多边形周长的比等于相似比延伸问题：探究：（1）如图 272-11（1），?ABC?A1B1C1，相似比为k1，它们的面积比是多少？让学生经历从特殊到一般的过程，体会有限数学归纳法的魅力，学生以小组讨论的形式开展学习有利于丰富学生的探究经验。名师精编优秀教案ABCDABCDA1B1C1D1（1）（2）图 272-11 分析：如图 27 2-11（1），分别作出?ABC 和?A1B1C1的高 AD和 A1D1。ADB=A1D1B1=900又 B=B1?ABD?A1B1D111111ADABkA DA B111ABCA B CSS1111111111111111221122BC ADKB CKA DB CA DB CA D=k12 相似三角形面积比等于相似比的平方（2）如图272-11（2），四边形ABCD 相似于四边形A1B1C1D1，相似比为k2，它们的面积比是多少？分析：111ABCA B CSS111ACDA C DSSk22 1111ABCDA B C DSS四边形四边形111111ABCACDA B CA C D+SSSSk22相似多边形面积比等于相似比的平方应用新知：例 6：如图 272-12，在?ABC 和?DEF 中，AB=2DE，AC=2DF，A=D，?ABC 的周长是24，面积是 48，求?DEF 的周长和面积。让学生经历从“相似三角形周长的比与相似比的关系到相似三角形面积比与相似比的关系”的过程，体会它们之间的形式雷同性与认知结构雷同性。让学生再次经历从特殊到一般的过程，进一步体验有限数学归纳法的魅力。文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9名师精编优秀教案图 272-12分析：?ABC 和?DEF 中，AB=2DE，AC=2DF 12DEDFABAC又 A=D?ABC?DEF，相似比为12?DEF 的周长=1224=12，面积=1()2248=12。让学生了解运用“相似三角形周长的比等于相似比、面积比等于相似比的平方”的常见解题思路。运用提高：1 P54练习题 1 2 P54练习题 2 让学生在练习中熟悉利用相似三角形周长的比等于相似比、面积比等于相似比的平方，解决简单的问题。课堂小结：说说你在本节课的收获。让学生及时回顾整理本节课所学的知识。布置作业：1 必做题：P54练习题 3，4 2 选做题：P57习题 272 题 12，13，14。3备选题：如图，已知矩形ABCD 的边长 AB=2，BC=3，点 P是 AD边上的一动点（P异于 A、D），Q是 BC边上的任意一点.连 AQ、DQ，过 P作 PE DQ交 AQ于 E，作 PF AQ交 DQ于 F.（1）求证：APE ADQ；（2）设 AP的长为 x，试求 PEF的面积 SPEF关于 x 的函数关系式，并求当P在何处时，SPEF取得最大值？最大值为多少？分层次布置作业，让不同的学生在本节课中都有收获。DEFABC文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9名师精编优秀教案（3）当 Q在何处时，ADQ 的周长最小？（须给出确定Q在何处的过程或方法，不必给出证明）备选题答案：（1）证APE=ADQ，AEP=AQD.（2）注意到 APE ADQ 与PDE ADQ，及SPEF=PEQFS平行四边形21，得SPEF=xx231=4323312x.当23x，即 P是 AD的中点时，SPEF取得最大值43.（3）作 A关于直线 BC的对称点A，连 DA 交 BC于 Q，则这个点 Q就是使 ADQ 周长最小的点，此时 Q是 BC的中点.设计思想：本节课主要是让学生理解并掌握相似三角形周长的比等于相似比、面积比等于相似比的平方，通过探索相似多边形周长的比等于相似比、面积比等于相似比的平方，体验化归思想，学会应用相似三角形周长的比等于相似比、面积比等于相似比的平方来解决简单的问题。因此本教学设计突出了“相似比相似三角形周长的比相似多边形周长的比”、“相似比相似三角形面积的比相似多边形面积的比”等一系列从特殊到一般的过程，以让学生深刻体验到有限数学归纳法的魅力。ABCDPEFQ文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 ZZ1U4G6J6B9文档编码:CD5H3H2N1G2 HP8B5R1B1K8 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