Since this is not my area of expertise, I searched Google under the key words "proof centroid of an equilateral triangle" to get this:
http://www.google.com/search?client=safari&rls=en&q=proof+centroid+of+an+equilateral+triangle&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
Use a two column proof to show that the centroid of an equilateral triangle divides the inside area into 6 congruent triangles
2 answers
that didn't really help...i was asking for a solution not a guide on how to search google.