Refresher - Concurrence Theorems

The four theorems are known as the concurrence theorems. They all involve the intersection of three types of line segments that are related to every triangle perpendicular bisectors of the sides, the medians, the altitudes and interior and exterior angle bisectors.

1. The perpendicular bisectors of the sides of a triangle meet at a point which is equally distant from the vertices of the triangle. The point of concurrence is called the circumcenter.
2. The bisectors of the angles of a triangle meet at a point that is equally distant from the sides of the triangle.
3. If we extend the sides of a triangle we can form external angles. The bisectors of the external angles on one side of a triangle and the bisector of the opposite internal angle are concurrent.
4. The medians of a triangle are concurrent and intersect each other in a ratio of 2:1.