How do medians locate a triangle's centroid?

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia. — geometry This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

In geometry, a median is defined as a line segment connecting a vertex of a triangle to the midpoint of the opposite side.1

The centroid is located at the point where all three medians of a triangle intersect. This point is significant because it represents the center of mass for a thin, uniformly dense object shaped like the triangle. Additionally, each individual median divides the triangle into two smaller triangles of equal area.1