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Lesson Similarity and scaling factor In a picture book of Goldilocks and the Three Bears, the papa bear is big, the mama bear is not so big, and the baby bear is small. In spite of the size, the three bears look much alike, although the artist may dress the mama bear with an apron and the baby bear with a red bow on its head. When people say, “the mother and daughter look alike,” they are probably imagining that if the daughter had instantly grown up to the size of mother, two are identical. The idea of “look alike” carries over to the geometric concept of similarity. We say objects are similar if one can somehow turn them into the same shape. For instance, triangle A and B in figure 1 are similar because they are indeed identical when the sides of triangle A are halved or triangle B is doubled. Here,
Figure 1. Right-angled triangles
the key word “halved” or “doubled” is actually carried out by scaling factor 1/2 or 2. Also, we must rotate triangle C to bring it similar to triangle A. In fact, one may exhibit similarity more directly by a copying machine with the option to reduce/enlarge than by a set of similarity conditions that you have learned in geometry. For instance, if triangle A in figure 1 is reduced by 50% (scaling factor = 1/2) it lies exactly on top of triangle B, and vice versa. |
