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

What is the length of line segment 𝐢𝐷?


Video Transcript

What is the length of line segment 𝐢𝐷?

On this diagram, we can go ahead and identify line segment 𝐢𝐷 as here. From there, it might be helpful to write out what we know based on this figure. We know that line segment 𝐡𝐸 is equal to line segment 𝐸𝐢. We also know that line segment 𝐡𝐹 is equal to line segment 𝐹𝐴. We know that line segment 𝐡𝐷, 𝐴𝐸, and 𝐢𝐹 all intersect at one point. And we know the measure of line segment 𝐴𝐢 is 13.8 centimeters.

What can we say based on this information? Because the point 𝐸 divides line 𝐡𝐢 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 𝐴𝐸 is a median. For that same reason, point 𝐹 is a midpoint, and so we can say line segment 𝐢𝐹 is a median because 𝐴𝐸 and 𝐢𝐹 are medians and line segment 𝐡𝐷 intersects at the same point as the other two medians. They have a point of concurrency, which makes line segment 𝐡𝐷 also a median and tells us that line segment 𝐴𝐷 will be equal in length to line segment 𝐷𝐢.

Then we know to find the value of line segment 𝐢𝐷, 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 𝐢𝐷 has a length of 6.9 centimeters.

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