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Similarity on a Euclidean Plane (SIM)

In: Euclidean Geometry and its Subgeometries

Author

Listed:
  • Edward John Specht

    (Indiana University South Bend)

  • Harold Trainer Jones

    (Andrews University)

  • Keith G. Calkins

    (Ferris State University)

  • Donald H. Rhoads

    (Andrews University)

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.

Suggested Citation

  • Edward John Specht & Harold Trainer Jones & Keith G. Calkins & Donald H. Rhoads, 2015. "Similarity on a Euclidean Plane (SIM)," Springer Books, in: Euclidean Geometry and its Subgeometries, edition 1, chapter 0, pages 319-333, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-23775-6_15
    DOI: 10.1007/978-3-319-23775-6_15
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