Euler Line Segment Investigation
The Euler Line is named after the 18th century Swiss mathematician Leonhard Euler who proved that three points of concurrency (circumcenter, centroid, and orthocenter) are collinear. Additionally, the centroid divides the Euler segment into two parts so that the smaller part is half the larger part. Play with the dimensions of the triangle below to explore this cool property!
What do you notice if the triangle is acute? What do you notice if the triangle is obtuse? What do you notice if the triangle is equilateral? What else is interesting?