# Question Video: The Properties of the Point of Concurrency of the Medians of a Triangle Mathematics • 11th Grade

In a triangle π΄π΅πΆ, π is the point of concurrency of its medians. If line segment π΄π· is a median, then π΄π = οΌΏ ππ·.

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### Video Transcript

In a triangle π΄π΅πΆ, π is the point of concurrency of its medians. If line segment π΄π· is a median, then π΄π is equal to blank of ππ·.

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 whatβs happening here, we would need triangle π΄π΅πΆ and then we could sketch a centroid. We know that the point of concurrency, the centroid, is point π and that line π΄π· 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 ππ· and π΄π. To go from ππ· to π΄π, to get from one-third to two-thirds, we multiply by two. π΄π is twice ππ·, which means we would find π΄π by multiplying ππ· by two.