Question

Q.) Prove that centroid of equilateral triangle divides the median in the ratio of 2 : 1.

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Answer 1

Let the medians AD, BE and CF of the triangle ABC intersect at G, the centroid of the triangle, and let the straight line AD be extended up to the point O such that 

AG = GO. 

Then the triangles AGE and AOC are similar (common angle at A, AO is twice AG, AC is twice AE), and so OC is parallel to GE. But GE is BG extended, and so OC is parallel to BG. Similarly, OB is parallel to CG. 

The figure GBOC is therefore a parallelogram. Since the diagonals of a parallelogram bisect one another, the point of intersection D between the diagonals GO and BC is such that GD = DO, and 

GO = GD + DO = 2GD. 

So, AG = GO = 2GD, 

or AG:GD = 2:1. 

This is true for every other median.

I hope it right

Advance happy New year

Answer 2

Heyaa folk !!




As we know centroid is formed when There ,the medians cut each other

Plzz see on attached image
Hope this helps u !!