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Triangles whose sides form an arithmetic progression

Published online by Cambridge University Press:  08 October 2020

Sadi Abu-Saymeh  and
Mowaffaq Hajja
Sadi Abu-Saymeh
Affiliation:
2271 Barrowcliffe Dr., Concord, NC 28027, USA e-mail: ssaymeh@yahoo.com
Mowaffaq Hajja
Affiliation:
P. O. Box 388 – Al-Husun, 21510 – Irbid – Jordan e-mail: mowhajja@yahoo.com
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Extract

This article is motivated by, and is meant as a supplement to, the recent paper [1]. That paper proves three geometric characterisations of triangles whose sides are in arithmetic progression, or equivalently triangles in which one of the sides is the arithmetic mean of the other two. More precisely, it gives three geometric contexts in which such triangles appear. In this Article, we supply references for the results in [1] and we provide more proofs of these results. We also add more contexts in which such triangles appear, and we raise related issues for future work. We hope that this will be a source of problems for training for, and for including in, mathematical competitions.

Type
Articles
Information
The Mathematical Gazette , Volume 104 , Issue 561 , November 2020 , pp. 469 - 481
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Copyright
© Mathematical Association 2020

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