Dynamic Construction of Triangle Medians and Proportional Relations

This example demonstrates the dynamic construction of triangle medians and their proportional relationships, visually showing how the intersection point (centroid) divides each median in a 2:1 ratio using a slider and scaling transformations. Core mathematical concepts include triangle medians, centroid, similar triangles, and segment proportions. Construction details: using GeoGebra commands such as Segment to draw triangle sides, Midpoint to construct midpoints, Dilate to scale vertices with a scale factor, and Angle to mark relevant angles; objects include vertices A, B, C, sides a, b, c, midpoints D, E, scaleFactor, and scaled points B', C', etc., with text objects displaying segment ratios (ratioBlue, ratioGreen, ratioPink) and median ratio (ratioMedians). Suitable for middle and high school geometry teaching, to understand the centroid property and dynamically verify proportional relations, also useful for exploring similar triangles and vector linear combinations.