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.

The definition of concurrent is when three or more lines meet at a single point. 

As we have four lines meeting at a single point (the centroid of a triangle), we meet the condition for concurrency.

I am at a loss on how to prove the validity of a definition.  Perhaps something is missing in the problem.  I suspect there may be as the determinant 'the' is used with the word triangle and no triangle that I can perceive is given by image, description. or specified characteristics that are not otherwise general to all triangles in normal, Euclidean space.

Posted by Dej Mar on 2008-03-08 08:48:30