Constructing an Angle Bisector + Interactive Activities

This example demonstrates, step by step, how to construct the angle bisector of a given angle and provides related open-ended exploration activities, including versions with and without GeoGebra. The key mathematics includes the angle bisector property (points on the bisector are equidistant from the angle’s sides), constructing intersection points using circles, and verifying symmetry via reflection. Construction approach in GeoGebra: create necessary points and auxiliary circles using Point and Circle; find circle-line or circle-circle intersection locations with Intersect; use Segment to define sides/segments and Min to select relevant key points under a constraint; compute the given angle with Angle; generate the bisector using AngularBisector; and use Mirror to confirm the bisector’s symmetry behavior. The model includes tracked points (e.g., k, O, A, B, C and others), segments (e.g., segmAB, segmAC), and circle/radius parameters (e.g., r1, R1, R2) together with interactive guidance (textInstr, multiple text labels) and slider/animation elements (aniSli, aniMin, aniMax). Suitable for middle-school geometry lessons, guided construction practice, and interactive classroom or group discovery activities.