Euler's Identity:

I will know explain how to find each of these three centers in a triangle in order to construct the Euler Line.

Another interesting fact about the Euler Line is that the distance between the orthocenter to the centroid is always twice as long as the distance from the centroid to the circumcenter. This webpage from the University of Georgia has a nice prove for showing that these three centers of a triangle lie on the same line, and that the distance between the orthocenter to the centroid is always twice as long as the distance from the centroid to the circumcenter.