Exterior Angle Bisector Theorem and Its Proof

This GeoGebra example demonstrates the exterior angle bisector theorem: when the bisector of an exterior angle of a triangle intersects the extension of the opposite side, it divides that side externally into segments proportional to the adjacent sides. The core mathematical concepts include the exterior angle bisector theorem, ratio and proportion, triangle side-angle relationships, and geometric proof. Construction highlights: using GeoGebra commands such as Line, Polygon, Point, AngularBisector, Intersect, Segment, and Angle to build the triangle, the exterior angle bisector, and its intersection with the extended opposite side; Distance command measures relevant segment lengths, and text objects display the ratio; dynamic points or sliders allow reshaping the triangle to verify the theorem universally. Suitable for middle and high school geometry classes, math competition training, and dynamic geometry exploration, helping students grasp the proof logic and proportional properties of the exterior angle bisector theorem.