Exploring the Points of Concurrency of a Triangle

This GeoGebra example demonstrates the four classical points of concurrency in a triangle: the centroid (intersection of medians), the incenter (intersection of angle bisectors), the circumcenter (intersection of perpendicular bisectors), and the orthocenter (intersection of altitudes). By dragging vertices A, B, and C, users can dynamically observe how these points move and relate to the triangle's shape. The core mathematical concepts include definitions of medians, angle bisectors, perpendicular bisectors, and altitudes, along with their concurrency properties. The construction uses GeoGebra commands such as Polygon to create triangle poly1, Midpoint and Line for medians, AngularBisector for angle bisectors, LineBisector for perpendicular bisectors, OrthogonalLine for altitudes, and Intersect to find the concurrency points (labeled D, E, F, G, H, I, J). This resource is suitable for middle school or high school geometry classes, serving as an interactive tool for teaching triangle centers and their properties, and for exploratory learning.