Abstract
This chapter defines a similarity mapping on a Euclidean plane as a dilation, an isometry, or a composition of a dilation and an isometry. Such mappings are used to define the similarity of two sets. Similarity is shown to be an equivalence relation, and criteria are developed for similarity of triangles. The chapter concludes with a proof of the Pythagorean Theorem, and a proof that the product of the base and altitude of a triangle is constant.
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© 2015 Springer International Publishing Switzerland
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Specht, E.J., Jones, H.T., Calkins, K.G., Rhoads, D.H. (2015). Similarity on a Euclidean Plane (SIM). In: Euclidean Geometry and its Subgeometries. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-23775-6_15
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DOI: https://doi.org/10.1007/978-3-319-23775-6_15
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-23774-9
Online ISBN: 978-3-319-23775-6
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