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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: mowhajja1234@gmail.com
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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
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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