Theorem 10.1.4

Theorem: The medians of a triangle are congruent and their point of concurrency is the point of trisection of each median.

Given: $\triangle{ABC}$, in which medians $\overline{BE}$ and $\overline{CF}$ met in G.

To Prove: i. $\overline{AG}$ produces bisect $\overline{BC}$ in D, and ii. G is the point of trisection of each median.

Construction: Draw $\overline{CH}||\overline{EB}$ meeting $\overline{AD}$ produced in H. Join points B and H.

Proof: