Students will see a proof of the incenter theorem, which says that the angle bisectors of a triangle intersect at a unique point that is equidistant from the sides of the triangle. Their point of intersection, is of course, the incenter. Students will also learn why the area of a triangle is equal to half its perimeter times the radius of its incircle. Before attempting to understand these proofs, students must know the angle bisector theorem. Students must also know the ASA and hypotenuse-leg congruence theorems.
The Incenter of a Triangle by Sean Johnston
Conclude by giving your students these challenges: