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 re(2): Can you provide insight? by Dej Mar)

After checking it out with Geometer's Sketchpad.

For parallelograms,
it looks like AA' and CC' define the same line as
do BB' and DD'. For all other quadrilaterals (
convex, concave, even reflex) the four lines
are concurrent. Note that for some quadrilaterals,
X = X' and we only have three lines. But, the three
lines are concurrent.

So maybe instead of saying that the four lines
are concurrent, we should say the "four" lines
pass through the same point. 

Edited on March 9, 2008, 4:53 am

Posted by Bractals on 2008-03-09 04:50:35