Medians of a Triangle and the Centroid

This GeoGebra example dynamically illustrates the medians of a triangle: each median connects a vertex to the midpoint of the opposite side, and all three medians intersect at a single point called the centroid (or barycenter). The key mathematical concept is that the centroid divides each median in a 2:1 ratio from the vertex to the midpoint. The construction uses GeoGebra commands such as Segment to draw the triangle sides and medians, Midpoint to locate the midpoints of the sides, Intersect to find the centroid, and Distance to measure the lengths from the centroid to vertices and midpoints, with text objects displaying these distances and ratios. Additional elements like rotation and angle tools may be used to explore related properties, possibly connecting to similarity transformations or the Pythagorean theorem. This resource is suitable for middle school and high school students learning triangle geometry, and for teachers demonstrating centroid properties in class.