Barycenter of a Triangle: Median Intersection and Proof

This GeoGebra example dynamically demonstrates the intersection point of the three medians of a triangle, known as the centroid or barycenter, and its fundamental property. The core mathematical concepts include medians, centroid, and the fact that the centroid divides each median in a 2:1 ratio from the vertex to the midpoint of the opposite side. Construction highlights: using GeoGebra, an arbitrary triangle is created, midpoints of each side are marked, and segments connecting each vertex to the opposite midpoint (medians) are drawn; the three medians concur at the centroid. By dragging vertices, users can observe that the centroid remains the intersection point regardless of triangle shape, and can verify the 2:1 division ratio using measurement or ratio tools. This resource is suitable for middle school to high school students learning plane geometry and triangle properties, as well as for teachers demonstrating the concurrency of medians and the proof of centroid properties in class.