What is the length of line segment
On this diagram, we can go ahead
and identify line segment 𝐶𝐷 as here. From there, it might be helpful to
write out what we know based on this figure. We know that line segment 𝐵𝐸 is
equal to line segment 𝐸𝐶. We also know that line segment 𝐵𝐹
is equal to line segment 𝐹𝐴. We know that line segment 𝐵𝐷,
𝐴𝐸, and 𝐶𝐹 all intersect at one point. And we know the measure of line
segment 𝐴𝐶 is 13.8 centimeters.
What can we say based on this
information? Because the point 𝐸 divides line
𝐵𝐶 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 𝐶𝐹 is a median because 𝐴𝐸 and 𝐶𝐹 are
medians and line segment 𝐵𝐷 intersects at the same point as the other two
medians. They have a point of concurrency,
which makes line segment 𝐵𝐷 also a median and tells us that line segment 𝐴𝐷 will
be equal in length to line segment 𝐷𝐶.
Then we know to find the value of
line segment 𝐶𝐷, 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
𝐶𝐷 has a length of 6.9 centimeters.