### Video Transcript

Find the length of line segment
π΄π, given that π΄πΈ equals 54.

Letβs see what we can tell from the
diagram. The point π· divides line segment
π΄π΅ in half, and the point πΈ divides line segment π΅πΈ in half. So we have two midpoints. And we know that π΄ and πΆ are
vertices of this triangle, which means that line segment π΄πΈ and line segment πΆπ·
are medians of this triangle. The place where medians intersect
inside a triangle is called the point of concurrency, or the centroid. And we know based on the centroid
theorem that the distance from the vertex to the centroid is two-thirds of the
median, and the distance from the centroid to the midpoint is one-third of the
median.

This means line segment π΄π is
equal to two-thirds the median π΄πΈ. And since we know π΄πΈ, the median,
equals 54, we can say that the length of line segment π΄π will be equal to
two-thirds of 54. If we wanna simplify this, I know
that 54 divided by three equals 18 and two times 18 equals 36. So we can say that line segment
π΄π measures 36.