The Euler Line
Leonhard Euler noticed that, in a triangle that is not equilateral, the Centroid, Circumcenter, and Orthocenter all lie on the same line. The Centroid being where the Medians intersect, Circumcenter being where the Perpendicular Bisectors intersect, and the Orthocenter being where the Altitudes intersect, all of which are shown below.
Drag points A, B, or C around to see how the Centroid, Circumcenter, and Orthocenter lie on the Euler Line no matter the shape of the triangle. Notice how when all the points meet the triangle is equilateral (Angles inside are all 60°). Use the check boxes to toggle the Medians, Perpendicular Bisectors and Altitudes.