CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS

Title & Authors
CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS
Kim, Dong-Soo; Lee, Kwang Seuk; Lee, Kyung Bum; Lee, Yoon Il; Son, Seongjin; Yang, Jeong Ki; Yoon, Dae Won;

Abstract
For a polygon P, we consider the centroid $\small{G_0}$ of the vertices of P, the centroid $\small{G_1}$ of the edges of P and the centroid $\small{G_2}$ of the interior of P, respectively. When P is a triangle, the centroid $\small{G_0}$ always coincides with the centroid $\small{G_2}$. For the centroid $\small{G_1}$ of a triangle, it was proved that the centroid $\small{G_1}$ of a triangle coincides with the centroid $\small{G_2}$ of the triangle if and only if the triangle is equilateral. In this paper, we study the relationships between the centroids $\small{G_0}$, $\small{G_1}$ and $\small{G_2}$ of a quadrangle P. As a result, we show that parallelograms are the only quadrangles which satisfy either \$G_0
Keywords
Language
English
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