Research article Special Issues

Side-side-angle triangle congruence axiom and the complete quadrilaterals

  • Received: 17 November 2022 Revised: 19 December 2022 Accepted: 21 December 2022 Published: 06 January 2023
  • Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.

    Citation: Peter Csiba, László Németh. Side-side-angle triangle congruence axiom and the complete quadrilaterals[J]. Electronic Research Archive, 2023, 31(3): 1271-1286. doi: 10.3934/era.2023065

    Related Papers:

  • Among the triangle congruence axioms, the side-side-angle (SsA) axiom states that two triangles are congruent if and only if two pairs of corresponding sides and the angles opposite the longer sides are equal. We construct two triangle sequences in which the items satisfy a modified condition. We require that the opposite angles of the shorter sides be equal. The locus of the intersection points of other sides of triangles is derived to be a hyperbola, and in a generalized form defined by a complete quadrilateral, it is a conic section.



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  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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