Question

proof of why centroid divides median in 2:1 ratio

Answer 1

heyate here we go
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Reflect the triangle along AC, you can get a diagram below:

ABCB1  is a parallelogram.

BEB1  is a straight line .

     Since  CD = AD1  and  CD // AD1, 

     DCD1A  is a parallelogram.  (opposite sides equal and parallel.)

\ DG // CG1 
Since  BD = DC and DG // CG1  \  BG = GG1   (intercept theorem)

BG : GG1 = 1 : 1

Since  GE = EG1 ,  BG : GE = 2 : 1.