The Median Lines (euclidean)
This next construction shows a triangle ABC with median lines. Median lines are lines that run through a point and bisects the segment opposite this point. We will once again examine the point of intersection of these medians. We will once again look to show that G will be contained within the boundaries of the triangle.
Theorem: If a triangle ABC has medians AE, BF, and CD (as drawn above), then G lies within the triangle. Proof: A proof similar to the previous page (angle bisectors) shows that the theorem holds.