Why the medians bisect the triangle
By: Tim Lehman

Each median splits the triangle into two equal pieces. By definition, each median connects a vertex to the midpoint on the opposite side. In the example above, D is the midpoint of segment AC. Thus, AD=DC. Also, the length between point B and segments AD and DC is the same because both segmets are colinear. Triangles ADB and DCB therefore have the same base and the same height. We then know they have the same area.