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Triangle Centers

There are a number of different triangle centers. There are four that we will be working with…incenter, circumcenter, centroid, and orthocenter. Keeping them all straight (no pun intended) can be daunting. Seriously!

Let's see if this helps!

incenter: the intersection of the ANGLE bisectors and a circle can be inscribed INSIDE the triangle

circumcenter: the intersection of the perpendicular bisectors of the SIDES and the center of the circumscribed circle (the circle goes AROUND the triangle)~this is the balancing point of the triangle

orthocenter: the intersection of the triangle's altitudes (*this is the only one not mentioned in Euclid's postulates)

  • altitude is the distance from one vertex to the opposite side forming a perpendicular line

centroid: the intersection of the triangle's medians

  • median is the distance from one vertex to the midpoint of the opposite side

Special Note: The orthocenter, incenter, and circumcenter are collinear and the line through these three points is called the Euler Line.

®2016 Sherry Skipper Spurgeon