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

Peter Csiba; László Németh; Peter Csiba; László Németh

doi:10.3934/era.2023065

Electronic Research Archive

2023, Volume 31, Issue 3: 1271-1286. doi: 10.3934/era.2023065

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

Peter Csiba ¹,
László Németh ^{2
,
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1.
Department of Mathematics, J. Selye University, Komárno 94501, Slovakia
2.
Institute of Informatics and Mathematics, University of Sopron, Sopron 9400, Hungary

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.
- triangle congruence,
- side-side-angle axiom,
- complete quadrilateral,
- 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

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Abstract

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.

References

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