Video: Understanding the Definition of the Median

Video Transcript

Find the length of line segment 𝐴𝑀, given that 𝐴𝐸 equals 54.

Let’s see what we can tell from the diagram. The point 𝐷 divides line segment 𝐴𝐵 in half, and the point 𝐸 divides line segment 𝐵𝐸 in half. So we have two midpoints. And we know that 𝐴 and 𝐶 are vertices of this triangle, which means that line segment 𝐴𝐸 and line segment 𝐶𝐷 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 𝐴𝑀 is equal to two-thirds the median 𝐴𝐸. And since we know 𝐴𝐸, the median, equals 54, we can say that the length of line segment 𝐴𝑀 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 𝐴𝑀 measures 36.