题目与解析
问题
三年级奥数题-数一数类型练习题:
数出右图中共有多少个三角形?
![](data:image/png;base64,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)
答案与解析
三年级奥数题-数一数类型练习题:
【思路导航】方法一:我们可以采用按边分类数的方法。以PA为边的三角形有:△PAB、△PAC、△PAD、3个;以PB为边的三角形还有:△PBC、△PBD 2个;以PC为边的三角形还有:△PCD 1个。所以,图中共有三角形3+2+1=6(个)。方法二:把图中三角形 △PAB、△PBC、△PCD看做基本三角形来数,那么,由1个基本三角形构成的三角形有:△PAB、△PBC、△PCD 3个;由2个基本三角形构成的三角形有: △PAC、△PBD 2个;由3个基本三角形构成的三角形有:△PAD 1个。所以,图中一共有3+2+1=6(个)三角形。方法三:我们发现,要数出图中三角形的个数,只需数出线段 AD中包含几条线段就可以了,即3+2+1=6(个)。所以图中共有6个三角形。
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