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图1中的两个三角形AB C和A′B′C′,它们的大小虽然不同,但是形状却是很象,如果仔细观察可以发现,这两个三角形的三个角都分别相等,即∠A=∠A′、∠B=∠B′和∠C=∠C′,并且,对应边成比例,即(AB)/(A′B′)=(BC/)/(B′C′)/(AC)/(A′C′)。在这两个三角形中间,用符号“。。”(读做“相似于”)连上,可写成△ABC ∽△A′B′C′,意思是,三角形ABC与三角形A′B′C′相似。判定两个三角形是不是相似,可根据以下三条定理中的任意一条确定:
The two triangles AB C and A’B’C’ in Fig. 1 are of different sizes, but their shapes are very similar. If you look closely, you can see that the three corners of the two triangles are equal, that is, A = ∠A’, ∠B = ∠B’, and ∠C = ∠C’, and proportional to the corresponding edge, that is, (AB)/(A’B’) = (BC/)/(B’C’) /(AC)/(A’C’). In the middle of these two triangles, the symbol “.” (“read like ” is similar to ") can be written as △ABC ∽ △A’B’C’, which means that the triangle ABC and the triangle A’ B’C’ is similar. To determine whether two triangles are similar, you can determine according to any of the following three theorems: