proof of why centroid divides median in 2:1 ratio
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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.
--------------------------
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.
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