Triangle Centroid Properties: Median Intersection and 2:1 Ratio

This GeoGebra example demonstrates the fundamental geometric properties of a triangle's centroid. The centroid G is the intersection point of the three medians AD, BE, and CF of triangle ABC. By constructing midpoints D, E, F and their corresponding medians, the example visually illustrates that the centroid divides each median in a 2:1 ratio, meaning the distance from a vertex to the centroid (such as AG) is exactly twice the distance from the centroid to the midpoint of the opposite side (such as GD). The applet includes distance measurements and text labels that dynamically update as users manipulate the vertices of the triangle, allowing learners to observe the invariant 2:1 ratio across all three medians regardless of how the triangle's shape changes. Through interactive dragging of vertices A, B, and C, students can explore how the centroid always remains the balance point of the triangle and consistently maintains equal area partitioning among the six small triangles formed by the medians. This hands-on exploration reinforces key geometry concepts including midpoints, medians, triangle centers, and proportional segments, making it an effective tool for reinforcing the centroid theorem in a visual and experiential manner suitable for secondary school geometry courses.