Centroid of a triangle

For proofs on the triangle, I let [math]\;\;[/math]The closed path [math]A→B→C[/math] [math]\;\;[/math]Side [math]{\rm a}[/math] be opposite vertex A However, it is often easier to use different labels (flip the switch): Taking A as the point of reference, Let the [math]{\rm b}= (B-A), {\rm c}=(C-A)[/math] So that [math]{\rm b}[/math] points to B, and [math]{\rm c}[/math] points to C. _______ To find the centroid of an [i]n[/i]-sided polygon (n-gon), I just break it up into triangles: [url]http://www.geogebratube.org/material/show/id/93239[/url]