8.2 Incenter (I) - concurrent at angle bisectors - incenter incircle inradius

Finding the incenter and creating the incircle of a triangle: Remember that the incenter is equidistant from the SIDES of the triangle. The distance from a point to a line is measured using the line that is PERPENDICULAR to the side passing through the point. A point that is equidistant from two sides of a triangle lies on the angle bisector. Why?

Incenter (I) - concurrent at angle bisectors - incenter incircle inradius