Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-12-01T03:29:01.767Z Has data issue: false hasContentIssue false
  • English
  • Français

The arbitrariness of the semi-angle-bisectors of a triangle

Published online by Cambridge University Press:  24 February 2022

Mowaffaq Hajja
Mowaffaq Hajja*
Affiliation:
Philadelphia University, Mobile: 0799342162, PO Box 388 (Al-Husun), 21510, Irbid, Jordan e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

Figure 1 shows a triangle ABC with the midpoints A′, B′ and C′ of its sides. The line segments AA′, BB′ and CC′ are called the medians, and the point G of their intersection the centroid. The line segments AG, BG and CG will be called, for lack of a better name, the semi-medians. It is interesting that the medians of any triangle can serve as the side lengths of some triangle. This property of the medians is referred to as the median triangle theorem in [1, §473, page 282], and is discussed, together with generalisations to tetrahedra and higher dimensional simplices, in [2].

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 565 , March 2022 , pp. 78 - 83
Check for updates
Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Johnson, R. A., Advanced euclidean geometry, Dover, (1929).Google Scholar
Al-Afifi, Gh., Hajja, M., Hamdan, A. and Krasopoulos, P., Pompeiu-like theorems for the medians of a simplex, Math. Ineq. Appl., 21 (2018), pp. 539–552.Google Scholar
Mironescu, P. and Panaitopol, L., The existence of a triangle with prescribed angle bisector lengths, Amer. Math. Monthly 101 (1994), pp. 58–60.10.1080/00029890.1994.11996906CrossRefGoogle Scholar
Dinca, G. and Mawhin, J., A constructive fixed point approach to the existence of a triangle with prescribed angle bisector lengths, Bull. Belg. Math. Soc. Simon Stevin, 17 (2010) pp. 333–341.10.36045/bbms/1274896209CrossRefGoogle Scholar
Osinkin, S. F., On the existence of a triangle with prescribed angle bisector lengths, Forum Geom. 16 (2016) pp. 399–405.Google Scholar
Heindl, G., How to compute a triangle with prescribed lengths of its internal angle bisectors, Forum Geom. 16 (2016) pp. 407–414.Google Scholar
Leversha, G., The Geometry of the Triangle, The United Kingdom Mathematics Trust (2013).Google Scholar
Habeb, J. M. and Hajja, M., A note on trigonometric identities, Expo. Math. 21 (2003) pp. 285–290.10.1016/S0723-0869(03)80005-1CrossRefGoogle Scholar