Geometric Construction of the Triangle Centroid

This GeoGebra example constructs a triangle and demonstrates how the centroid (Schwerpunkt) appears as the intersection point of the medians. It visualizes the key phenomenon: the centroid is precisely the common point where the medians meet, linking vertices to the midpoints of opposite sides. The main concepts include triangle medians and the centroid’s geometric meaning (and its role in defining characteristic segment ratios). In the construction, Intersect is used to compute the intersection point(s) that represent the centroid (e.g., object S), while Polygon, Segment, and Point create the triangle’s structure and the median segments (objects such as A, B, C, D, E, and related points). Circle is included for auxiliary constructions to locate midpoints or guide the construction (objects like c, d and associated auxiliary parameters). Suitable for middle and high school geometry lessons, classroom demonstrations, and student-led exploration of centroid properties through geometric construction.