Journal of Geometry

, 110:36 | Cite as

An algebraic characterization of properly congruent-like quadrilaterals

  • Giuseppina Anatriello
  • Francesco Laudano
  • Giovanni VincenziEmail author


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.


Quadrilaterals Congruence theorems Congruent-like quadrilaterals Properly congruent-like quadrilaterals 

Mathematics Subject Classification

51M04 51M05 97G40 


Compliance with ethical standards

Conflict of interest

No potential conflict of interest was reported by the authors.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di di ArchitetturaUniversità di Napoli “Federico II”NapoliItaly
  2. 2.Liceo Scientifico RomitaCampobassoItaly
  3. 3.Dipartimento di MatematicaUniversità di SalernoFiscianoItaly

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