Centroid of a Triangle: Geometric Construction and Properties by Sarah Marsh

① This example demonstrates how to construct the centroid of an arbitrary triangle in GeoGebra and shows that the centroid divides each median in a 2:1 ratio. ② Core mathematical concepts include triangles, medians, centroid, segment ratios, and the concurrency theorem in plane geometry. ③ Construction highlights: Polygon creates the triangle; Midpoint finds the three side midpoints; Segment draws the three medians connecting vertices to opposite midpoints; Intersect computes the common intersection point of the medians, which is the centroid. Key objects are vertices A, B, C, polygon poly1, midpoints D, E, F, medians f, g, h, and intersection G. ④ Suitable for middle‑school geometry (grades 7‑9) when teaching triangle centers, and also for high‑school analytic geometry or geometric construction practice to help students visualize the centroid’s construction and properties.