Dynamic Exploration of Triangle Centroid and Geometric Properties

This GeoGebra example dynamically demonstrates the definition, geometric construction, and movement of the centroid of a triangle as its vertices are dragged. Core mathematical concepts include the centroid (barycenter), intersection of medians, and general triangle center geometry. To construct this, the `Polygon` command is used to define the triangle `poly1`, while `Segment` and `LineBisector` (along with `Intersect`) are employed to locate the intersection of medians (the centroid) and other centers like the `Circumcenter`. Additional tools like `Circle` and `Angle` help visualize auxiliary geometric elements. It is highly suitable for secondary school geometry, coordinate geometry, or physics classes investigating the properties of triangle centers.