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More characterisations of parallelograms

Published online by Cambridge University Press:  16 February 2023

Mowaffaq Hajja  and
Panagiotis T. Krasopoulos
Mowaffaq Hajja
Affiliation:
P. O. Box 388 (Al-Husun), Irbid, 21510 Jordan e-mail: [email protected]
Panagiotis T. Krasopoulos
Affiliation:
Department of Informatics, KEAO Electronic National Social Security Fund 12 Patision Street, 10677 Athens, Greece e-mail: [email protected], [email protected]
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Several years ago, Professor Martin Josefsson told the first-named author, in a private communication, that his ‘characterisations of’ and ‘properties of’ series of papers that comprised tangential, extangential, bicentric, orthodiagonal, equidiagonal, and bisect-diagonal quadrilaterals, and rhombi and trapezoids, did not include parallelograms because the many characterisations of these figures are well known and are easily accessed via the net, and that nothing interesting can be added. In this Article, we present some characterisations of parallelograms that are very likely unknown and that will hopefully appeal to the readers of the Gazette. Other interesting characterisations that we have obtained and that could not find their place here are intended to form the material of another Article.

Type
Articles
Information
The Mathematical Gazette , Volume 107 , Issue 568 , March 2023 , pp. 76 - 83
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Copyright
© The Authors, 2023. Published by Cambridge University Press on behalf of The Mathematical Association

References

Pop, O. T., Minculete, N. and Bencze, M., An introduction to quadrilateral geometry, Editura Dedicata si Pedagigica, Romania (2013).Google Scholar
Smith, G. C., A mathematical olympiad primer (2nd edn), UKMT (2007).Google Scholar
Andreescu, T., Feng, Z. and Lee, G. Jr., Mathematical Olympiads 2000-2001, Problems and solutions from around the world, Mathematical Association of America (2003).CrossRefGoogle Scholar
Josefsson, M., Properties of bisect-diagonal quadrilaterals, Math. Gaz. 101 (July 2017) pp. 214–226.CrossRefGoogle Scholar
Hajja, M., Problem 1002, College Math. J., 44 (2013), p. 233: Correction, ibid, 44 (2013), p. 437: Solution, ibid, 45 (2014), pp. 394-395.Google Scholar
Honsberger, R., More mathematical morsels, Dolciani Math. Expositions, No. 10, Mathematical Association of America (1991). CrossRefGoogle Scholar
Dörrie, H., 100 great problems in elementary mathematics, Dover (1965).Google Scholar
Casey, J., A sequel to Euclid (5th edn.), Longmans, Green & Co. (1888).Google Scholar
Larson, L. C., Problem-solving through problems, Springer (1983).CrossRefGoogle Scholar