2021秋北师版九年级上数学4.4.3探索相似三角形的条件（SSS）导学案（无答案）

2021秋北师版九上数学4.4.3探索相似三角形的条件导学案
【学习目标】
1．掌握三边对应成比例判定两个三角形相似的方法．
2．会选择合适的三角形相似的判定方法解决简单问题．
【学习重点】
掌握相似三角形的判定定理：“三边成比例的两个三角形相似”．
【学习难点】
会准确运用三角形相似的判定定理来判断、证明及计算．
情景导入　生成问题
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1．两角分别 的两个三角形相似；两边成比例且夹角相等的两个三角形相似．
2．下列说法正确的是(　 )
A．有一个角相等的两个等腰三角形相似
B．所有的直角三角形相似
C．有一个锐角对应相等的两个直角三角形相似
D．所有的等腰三角形相似
3．已知△ABC如图所示，则与△ABC相似的是图中的(　 　)
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自学互研　生成能力
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师：我们上两节课学过什么定理？
师生共同回忆，在上两节课的探索中，我们知道：三角对应相等、三边对应成比例的两个三角形相似；两角分别相等的两个三角形相似；两边成比例及夹角相等的两个三角形相似．
师：那么判定三角形相似还有没有其他条件呢？今天我们再次踏上探索之旅途．
画△ABC与△A′B′C′，使、和都等于给定的值k.
(1)设法比较∠A与∠A′的大小．
(2)△ABC与△A′B′C′相似吗？说说你的理由．
改变k值的大小，再试一试．
生：按照上面的步骤进行，这里的k由自己定，为了节约时间，一个组取一个相同的k值，不同的组取不同的k值．
内容：学生根据画出的相似三角形的图形及在画相似三角形中的“发现”进行相互交流，教师给予适当的帮助，后由学生展示、讲解画出来的相似三角形，展示自己探索的过程及自己得出的结论．
师：经过大家的亲身参与体会，你们得出的结论是什么呢？
生：结论为∠A＝∠A′，△ABC∽△A′B′C′，理由是：∠A＝∠A′，＝.
根据“两边成比例及夹角相等的两个三角形相似”可知：△ABC∽△A′B′C′.
师：其他组的同学的结论相同吗？
生：相同．
师：经过大家的探讨，我们又掌握了一种相似三角形的判定方法．
师：(演示课件)
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判定定理3：三条边成比例的两个三角形相似．
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1．自学自研教材P94页的例3.
2．完成教材P94的随堂练习．
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师：幻灯片展示：如图，△ABC与△A′B′C′相似吗？你有哪些判断方法？
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生：先独立思考，然后小组合作交流．
解：△ABC∽△A′B′C′.
判断方法有：1.三边成比例的两个三角形相似；2.两角分别相等的两个三角形相似；3.两边成比例且夹角相等的两个三角形相似；4.定义法．
目的：巩固对本节知识的理解；并让学生将上两节课：相似三角形的判定定理1、2，与本课知识：相似三角形的判定定理3的内容系统的掌握．
对应练习：
1．教材P95页习题4.7第1题．
解：∵＝，＝，＝.∴＝＝，∴这两个三角形相似．
2．教材P95页习题4.7第2题．
答：△ABC∽△EFG.利用判定定理3.
交流展示　生成新知
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1．将阅读教材时“生成的问题”和通过“自主探究、合作探究”得出的“结论”展示在各小组的小黑板上．并将疑难问题也板演到黑板上，再一次通过小组间就上述疑难问题相互释疑．
2．各小组由组长统一分配展示任务，由代表将“问题和结论”展示在黑板上，通过交流“生成新知”．
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知识模块一　探索三边成比例的两个三角形相似
知识模块二　判定定理3的应用
检测反馈　达成目标
1．下列条件不能判定△ABC与△ADE相似的是( )
A.＝，∠CAE＝∠BAD
B．∠B＝∠ADE，∠CAE＝∠BAD
C.＝＝
D.＝，∠C＝∠E
2．下列四个三角形，与右图中的三角形相似的是( 　)
,A)　　　　　,B)
,C) ,D)
3．网格图中每个方格都是边长为1的正方形．若A，B，C，D，E，F都是格点，试用三边对应成比例的方法说明△ABC∽△DEF.
课后反思　查漏补缺
1．收获：________________________________________________________________________
2．存在困惑：________________________________________________________________________