Question Video: Finding a Side Length in a Triangle Using Properties of Medians | Nagwa Question Video: Finding a Side Length in a Triangle Using Properties of Medians | Nagwa

# Question Video: Finding a Side Length in a Triangle Using Properties of Medians Mathematics • Second Year of Preparatory School

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In β³π½πΎπΏ, π½π = 6 cm. Find the length of line segment ππ.

01:50

### Video Transcript

In triangle π½πΎπΏ, π½π equals six centimeters. Find the length of line segment ππ.

We need to know the length of line segment ππ, and weβve been given that π½π equals six centimeters. First of all, we should note that the point π divides the line segment πΎπΏ in half, which makes π a midpoint. Since π½ is a vertex of this triangle, we know that the distance between a vertex and the midpoint is called the median. And so we can say that π½π is a median. In the same way, π divides line segment π½πΏ and π divides line segment π½πΎ, which means πΎπ is a median and πΏπ is a median. Since π½π, πΎπ, and πΏπ are all meet at one point π, π is the point of concurrency or the centroid.

This is important because we know something about the centroid. For a median, the distance between the vertex and the centroid is two-thirds of the median. And the distance between the centroid and the midpoint is one-third of the distance of that median. To go from two-thirds to one-third, we multiply by one-half. One-third is half of two-thirds. And so we can say that the line segment ππ will be equal to one-half the line segment π½π. Since π½π was equal to six centimeters, we take one half of that and we say that the line segment ππ is equal to three centimeters.

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