Video: Understanding the Definition of the Median

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

01:32

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 𝐴𝐡 in half, and the point 𝐸 divides line segment 𝐡𝐸 in half. So we have two midpoints. And we know that 𝐴 and 𝐢 are vertices of this triangle, which means that line segment 𝐴𝐸 and line segment 𝐢𝐷 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.

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