Incenter - Jenna Means

① This example demonstrates the construction of the incenter of a triangle and its associated angle bisectors, perpendicular segments, and angle labels in GeoGebra. ② Core mathematical concepts include the definition of the incenter as the intersection of internal angle bisectors, properties of angle bisectors, the inradius (distance from incenter to sides), and angle measurement. ③ Construction details: the Polygon command creates triangle ABC; AngularBisector constructs the three internal angle bisectors; Intersect finds their common point D (the incenter); Angle labels angles α, β, etc.; Segment connects vertices to the incenter; OrthogonalLine draws perpendiculars from the incenter to sides, revealing the inradius; text objects annotate the figure. ④ Suitable for middle school to high school students learning triangle centers, angle bisector theorems, and geometric construction, as well as for classroom demonstrations by teachers.