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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What is the length of line segment πΆπ·?

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### Video Transcript

What is the length of line segment πΆπ·?

On this diagram, we can go ahead and identify line segment πΆπ· as here. From there, it might be helpful to write out what we know based on this figure. We know that line segment π΅πΈ is equal to line segment πΈπΆ. We also know that line segment π΅πΉ is equal to line segment πΉπ΄. We know that line segment π΅π·, π΄πΈ, and πΆπΉ all intersect at one point. And we know the measure of line segment π΄πΆ is 13.8 centimeters.

What can we say based on this information? Because the point πΈ divides line π΅πΆ in half, this is a midpoint, and the distance from a vertex to a midpoint is a median. That means we can say that line segment π΄πΈ is a median. For that same reason, point πΉ is a midpoint, and so we can say line segment πΆπΉ is a median because π΄πΈ and πΆπΉ are medians and line segment π΅π· intersects at the same point as the other two medians. They have a point of concurrency, which makes line segment π΅π· also a median and tells us that line segment π΄π· will be equal in length to line segment π·πΆ.

Then we know to find the value of line segment πΆπ·, it will be equal to half of 13.8. And 13.8 times one-half is 6.9. And so we say that the line segment πΆπ· has a length of 6.9 centimeters.

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