Prove that the four lines obtained by joining each vertex of a quadrilateral to the centroid of the triangle determined by the other three vertices are concurrent.

(In reply to Can you provide insight? by Dej Mar)

Let ABCD be the quadrilateral.

Let A' be the centroid of triangle BCD.
Let B' be the centroid of triangle CDA.
Let C' be the centroid of triangle DAB.
Let D' be the centroid of triangle ABC.

We want to show that AA', BB', CC', and
DD' are concurrent.

Posted by Bractals on 2008-03-08 14:42:32