How to prove that the centroid of a triangle divides the median in the

1.	How to prove that the centroid of a triangle divides the median in the ratio 2:1??
Answer» \tThe Theorem\xa0D, E, F\xa0are\xa0mid-points of BC, CA, AB.AD, BE and CF are medians.The medians cut each others are\xa0centroid G\xa0.We need to show that:\xa0AG : GD = BG : GE = CG : GF = 2 : 1\xa0\xa0\xa0\xa0\xa0Simple Proof\xa0Reflect the triangle along AC, you can get a diagram below:\xa0\xa0ABCB1 is\xa0a parallelogram.BEB1 is\xa0a straight line . Since CD = AD1 and CD // AD1,\xa0 DCD1A is\xa0a parallelogram. (opposite\xa0sides equal and parallel.)\\\xa0DG // CG1\xa0 Since BD = DC and DG // CG1\\ BG = GG1 (intercept theorem)BG : GG1\xa0= 1 : 1Since GE\xa0= EG1\xa0, BG : GE = 2 : 1.\t

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