1. ## Centriod Theorem Problem

From this picture,

Find the length of line DG.

Line AG= 13x-3
line BG= 4x + 3
line CG= 3x + 14
line EG= 11

I figured BG = CG, so I set them equal and got x= 11.
I plugged the x value into everything, reviewed the centriod theorem formulas (e.g. line AD $\frac{2}{3}$ = AG )

2. There doesn't seem to be any reason why BG should be equal to CG.

If G is the centroid then BG = 2*GE (because $BG = \tfrac23BE$ and $GE = \tfrac13BE$). That will give you an equation for x.