HISTORY OF TRIANGLE CENTERS
The incenter, centroid, circumcenter, and orthocenter were discovered by the ancient Greeks. Somebody had bisected the angles of a triangle in the sand and noticed that they came together at one point. He proceeded by doing the same thing with an obtuse triangle. He got the same result. Continuing the process, with different triangles, he concluded that the 3 bisectors of a triangle will always meet and one point.
OTHER INTERESTING FACTS
The triangles formed from drawing the centroid all have equal areas.
All the triangle centers can be found by drawing only two lines.
The centroid is located two-thirds of the way from the vertex to the opposite midpoint.