**Trisections of the **

**Areas of
Triangles**

by

Nikki Bacon

**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.