If G is the centroid of triangle ACE, AG = 8, GF = 7, BG = 5, find each measure.

GD = 4
AD = 12
CG = 14
GE = 10
BE = 15
Explanation:Because G is the centroid, then the following are correct
CG : GF = 2 : 1
AG : GD = 2 : 1
GE : BG = 2 : 1
So to find
GD, given AG = 8, we have:
8/GD = 2/1
GD = 8/2 = 4
AD = AG + GD
= 8 + 4
= 12
CG/GF = 2/1
CG/7 = 2/1
CG = 14
GE/BG = 2/1
GE/5 = 2/1
GE = 10
BE = GE + BG
= 10 + 5
= 15