Side

Given:

First, trisect m(**a**) and m(**b**). **Click
here** if you need help trisecting a segment. We know the
centroid is 2/3 of the length of m(**a**) away from vertex
A. Also, the centroid is 1/3 of the distance of m(**b**) away
from the midpoint of side b. Thus, the centroid (point X below)
is at the intersection of the two circles centered at A and the
midpoint of **b** with a radius of 2/3 of m(**a**) and 1/3
of m(**b**), respectively. So, to start the construction, we
draw side **b** and the two circles.

Because both medians must go through the centroid, we can now
draw both medians. Further, by definition, the endpoint of m(**b**)
must be the vertex B. Therefore, we can construct the triangle.

**Click here** for a GSP sketch.