is a triangle where point bisects , point , and .
Draw to intersect at point . If cm, find the length of .
Draw a diagram to match the problem.
A median of a triangle is a line segment drawn from any vertex of the triangle to the midpoint of the opposite side. Since is the midpoint of , is a median of the triangle.
The point that divides a median by the ratio of from the base is the point of intersection of the triangle's medians. Since , point is the point of intersection of the medians.
passes through the point (the point of intersection of the medians), so it must be a median, too.
Since the point of intersection divides median by the ratio from the base, the length of must be a third of the length of .