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.



    加载中


    [1] J. Donnelly, The equivalence of Side–Angle–Side and Side–Angle–Angle in the absolute plane, J. Geom., 97 (2010), 69–82. https://doi.org/10.1007/s00022-010-0038-y doi: 10.1007/s00022-010-0038-y
    [2] J. Donnelly, The equivalence of Side–Angle–Side and Side–Side–Side in the absolute plane, J. Geom., 106 (2015), 541–550. https://doi.org/10.1007/s00022-015-0264-4 doi: 10.1007/s00022-015-0264-4
    [3] J. F. Rigby, Congruence axioms for absolute geometry, Math Chronicle., 4 (1975), 13–44. Available from: https://www.thebookshelf.auckland.ac.nz/docs/Maths/PDF/mathschron004-003.pdf.
    [4] H. Hähl, P. Peter, A variation of Hilbert's axioms for Euclidean geometry, Math. Semesterber., 69 (2022), 253–258. https://doi.org/10.1007/s00591-022-00320-3 doi: 10.1007/s00591-022-00320-3
    [5] H. S. M. Coxeter, Projective Geometry, Springer, 1987. Available from: https://link.springer.com/book/9780387406237.
    [6] E. Fortuna, R. Frigerio, R. Pardini, Projective Geometry–-Solved Problems and Theory Review, Springer, 2016. https://doi.org/10.1007/978-3-319-42824-6
    [7] Maplesoft, A division of Waterloo Maple Inc., Maple, 2022. Available from: https://www.maplesoft.com/products/.
    [8] P. Csiba, L. Németh, SSA Supplement Files, 2023. Available from: http://matematika.emk.uni-sopron.hu/en_GB/ssa.
  • Reader Comments
  • © 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2791) PDF downloads(131) Cited by(1)

Article outline

Figures and Tables

Figures(6)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog