In this lesson, students explore properties of angle bisectors. To build intuition, students first observe that pouring salt on a triangle forms ridges that meet at a peak, and the ridges appear to be angle bisectors. Students go on to prove that a point is on an angle bisector if and only if it is equidistant from the rays that form the angle. Then they show that all three angle bisectors of a triangle meet at a single point, the incenter of the triangle. This will lead to constructing a triangle’s inscribed circle in a subsequent lesson.

Students create viable arguments (MP3) when they use what they know about triangle congruence to prove facts about angle bisectors.