+159 G is the centroid of triangle ABC and D and E are the midpoints of line AB and line AC, respectively. line AG and line DE intersect at M. Find GM/GA.
+129852 
AE and AD divide sides AB and AB proprtionally
Therefore....DE is parallel to BC
And angle FAC = angle MAE
And since AF is a transversal cutting parallel lines DE and BC, then angle AME = angle AFC
So.....byAA concruency, triangle AME is simiar to triangle AFC
But since AE = 1/2 AC....then AM = (1/2) AF
And since G is a centroid, then AG = (2/3)AF
Then GM = AG - AM = (2/3)AF - (1/2)AF = (1/6)AF
Therefore GM : GA = (1/6)AF / (2/3)AF = (1/6) / (4/6) = 1 : 4
