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

Autor:	Peter Csiba, László Németh
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	triangle congruence side-side-angle axiom complete quadrilateral conic section Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 31, Iss 3, Pp 1271-1286 (2023)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2023065?viewType=HTML
Popis:	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.
Databáze:	Directory of Open Access Journals
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