AD is the mid point of triangle ABC and G divides AD in the ratio 2:1 .Prove that triangle AGB =area BGC = area AGC =1÷3 area ABC

Answer 1

label all your stuff
since BD = CD, area BDG = area DGC = x
since DG : GA = 1 : 2
area of BDG : BGA = 1 : 2 = x : 2x

label area of triangle BGA as 2x same for triangle AGC
so triangle BGC = 2x
triangle AGC = 2x
triangle ABC = 6x
so triangle AGC = 2x/6x = 1/3

Answer 2

btw, do you realize that G is the centroid of the triangle ?