Proving that the centroid is 2-3rds along the median | Geometry | Khan Academy

Showing that the centroid divides each median into segments with a 2:1 ratio (or that the centroid is 2/3 along the median)

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[linnthwin]

Man im in my second year of Mechanical Engineering and I still need this <3

[balakrishnakarri]

Good... but u have to explain also proof of those all 6 triangle's area is same

[clownphabetstrongwoman]

Draw 3 parallels for each triangle sides through the center, obtain a bunch of small congruent triangles and you can demonstrate (without any calculation), one by one each median, that medians intersect at 2/3 distal from the angles.

[srikanthchaturvedula]

Respected Sir,
In triangle AEB, you have made two sub triangles AEG and AGB
For triangle AGE, Area = 0.5*(base)*(perpendicular height to the base)
In this case if EG is the base, and AB is the height, how is EG perpendicular to AB ??
EB(of wich EG is a part) is just a median and it cannot be Perpendicular to AB

Thanks in advance

[peterlohnes]

Except you have to prove all those triangles have equal area.

[ishdx]

there goes my 1 hour of tinkering entirely using algebra, whithout any result because I couldn't cancel out variables

[someonetoogoodforyou]

I used to be atheist, but then i realized you ARE GOD!

[shishKumar]

Sir how could you mention AB as perpendicular
Please reply

[surajdixit]

does anybody got formal proof for this

[xSixPathsofPainx]

This isn't highschool geometry is it...