VARIOUS CENTROIDS OF QUADRILATERALS WITHOUT SYMMETRY

Abstract

For a quadrilateral P , we consider the centroid G0 of the vertices of P , the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P , respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

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