How do I prove the centroid of a triangle and its medial triangle using the vector method?

Given that the vertices of the medial are located at the side mid-points of triangle ABC.
Given an arbitrary point O that is not a vertex
Given the location of the centroid of triangle ABC is the vector (vector OA + vector OB + vector OC)/3.

How do I prove using the 'vector method" that a triangle and its medial triangle have the same centroid?