Question

prove median is devided in ratio of 2: 1 from centroid

Answer 1

D, E, F are mid-points of BC, CA, AB.

AD, BE and CF are medians.

The medians cut each others are centroid  G .

We need to show that:

AG : GD = BG : GE = CG : GF = 2 : 1

Reflect the triangle along AC
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.



HOPE THIS IS IT....