An angle bisector splits the angles of a triangle into two congruent parts. Drag the vertices of the triangle below to explore the perpendicular bisector.
All three angle bisectors meet at a point. The point of concurrency for the angle bisectors is called the incenter. Can the incenter be outside the triangle? If so, when?
Using the triangle above, create perpendicular segments from the incenter to each side of the triangle. First make a perpendicular line, make the intersection point where the right angle is and then measure from each point to the incenter. Move the vertices around. What did you find?
They are all the same length.