The medial triangle of a triangle ABC is the triangle with vertices at the midpoints of the sides ...

The medial triangle of a triangle ABC is the triangle with vertices at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, the location of the centroid is given by (vector OA + vector OB + vector OC)/3. Prove that the medial triangle shares the same centroid?