Triangle Centroid and Median Ratio (2:1)

This example demonstrates how the centroid of a triangle divides a median in the fixed ratio 2:1. It visualizes the key points on the median and annotates the corresponding segment lengths to confirm the relationship. The central mathematical ideas are triangle centroid (barycenter), medians, and the distance-ratio property that leads to the 2:1 split (often explained via mass points or vector reasoning). Construction highlights include using Polygon to draw triangle ABC, Midpoint to locate the midpoint D of side BC, and Segment to construct the median AD. Intersect and Distance are then used to obtain the relevant centroid-related point and compute lengths such as BD and DC (and also AG and GD), while Text objects label the measured distances and the expected 2:1 ratio. Suitable for middle school to high school geometry lessons and for students exploring centroid properties through dynamic geometric construction.