Centroid of a Triangle: Geometric Construction

① This example demonstrates how to construct the centroid (center of mass) of a triangle using geometric construction, which is the intersection point of the three medians. ② The core mathematical concept is the centroid property: it divides each median in a 2:1 ratio and represents the average of the three vertex coordinates. ③ Construction details: from the summary, the GeoGebra commands used are Segment, Midpoint, and Intersect. The triangle vertices A, B, C are defined, then midpoints D, E, F of the sides are created, medians i, j, k are drawn by connecting each vertex to the opposite side's midpoint, and their intersection point G (or H) is found as the centroid. ④ Suitable for middle school geometry or introductory high school coordinate geometry, helping students visually grasp the existence and uniqueness of the centroid and the concurrency of medians.