Hi everybody

Show that the centroid of a triangle coincides with that of the triangle formed by the mid points of the sides.

Thank you all

Sridhar

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- Jan 28th 2010, 12:23 AMyshridharcentriod of trianlge
Hi everybody

Show that the centroid of a triangle coincides with that of the triangle formed by the mid points of the sides.

Thank you all

Sridhar - Jan 28th 2010, 02:39 AMHallsofIvy
For a triangle, the centriod is just the "average" of the vertices. That is, if the vertices are , , and , in some coordinate system, then the centroid is at .

Of course, the midpoints of the sides are , , and . Use the formula above to find the centroid of that triangle.