I used SMART software to make this construction. Open the compass past the estimated midpoint of the side. Strike an arc. Keeping the same setting, move to the vertex on the opposite side of the side you are working with. Strike an arc such that it intersects the first arc twice. Use a straightedge to find the midpoint of the side. Draw a segment from that midpoint to the opposite vertex.
Do this for all three sides and you'll find the centroid of the triangle!