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An algebraic characterization of properly congruent-like quadrilaterals

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Abstract

In this paper, we will provide a characterization of pairs of non-congruent quadrilaterals for which all elements are pairwise congruent (‘properly congruent-like quadrilaterals’). As a consequence of this main result, we demonstrate a method to establish, given a generic quadrilateral, whether some quadrilaterals that are properly congruent-like to it exist and, if so, how to determine the values of their elements. In particular, this approach allows us to provide examples of quadrilaterals that are not congruent-like to any other quadrilateral and to show constructive examples of pairs of properly congruent-like quadrilaterals.

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Authors and Affiliations

  1. Dipartimento di di Architettura, Università di Napoli “Federico II”, Via Monteoliveto, 3, 80134, Napoli, Italy

    Giuseppina Anatriello

  2. Liceo Scientifico Romita, Via Facchinetti, 86100, Campobasso, CB, Italy

    Francesco Laudano

  3. Dipartimento di Matematica, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Giovanni Vincenzi

Authors
  1. Giuseppina Anatriello
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  2. Francesco Laudano
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  3. Giovanni Vincenzi
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Correspondence to Giovanni Vincenzi.

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Anatriello, G., Laudano, F. & Vincenzi, G. An algebraic characterization of properly congruent-like quadrilaterals. J. Geom. 110, 36 (2019). https://doi.org/10.1007/s00022-019-0493-z

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  • DOI: https://doi.org/10.1007/s00022-019-0493-z

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