Trisections of the

Areas of Triangles

by

Nikki Bacon

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1. Given a triangle ABC, find a point D such that line segments AD, BD, and CD trisect the area of the triangle into three regions with equal areas. Define D and prove that the triangle is divided into three regions of equal area. Show a construction for finding D.

I constructed triangle ABC and the segment BE which is a median of traingle ABC.

The point that divides the median of a triangle in the ratio of 2 : 1 is called the centroid of a triangle. The point D that I constructed above is the centroid of the triangle. To see a construction of the centroid of a triangle, click here.

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