Question Video: The Properties of the Point of Concurrency of the Medians of a Triangle Mathematics • Second Year of Preparatory School

Video Transcript

In a triangle 𝐴𝐵𝐶, 𝑀 is the point of concurrency of its medians. If line segment 𝐴𝐷 is a median, then 𝐴𝑀 is equal to blank of 𝑀𝐷.

First of all, we know that the point of concurrency of its medians in a triangle is its centroid. If we wanted to sketch a triangle to try and understand what’s happening here, we would need triangle 𝐴𝐵𝐶 and then we could sketch a centroid. We know that the point of concurrency, the centroid, is point 𝑀 and that line 𝐴𝐷 is a median. The centroid theorem tells us 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. And we want to compare the relationship between 𝑀𝐷 and 𝐴𝑀. To go from 𝑀𝐷 to 𝐴𝑀, to get from one-third to two-thirds, we multiply by two. 𝐴𝑀 is twice 𝑀𝐷, which means we would find 𝐴𝑀 by multiplying 𝑀𝐷 by two.