Center of Gravity of a Triangle Proof

[cookiesyum]

Homework Statement

The "center of gravity" of the triangle with vertices at A, B, and C is the point 1/3(A+B+C). Show that the center of gravity of a triangle is always the same as that of the triangle formed by the midpoints of its sides.

Homework Equations

The Attempt at a Solution

I have no idea where to even begin. =/ I drew the triangle formed by the midpoints of the sides and called it DEF...

 

[Dick]

The midpoint D of the side AB is D=(A+B)/2. Etc.

 

[cookiesyum]

Thanks for the hint!