Video Transcript
What is the length of line segment
πΆπ·?
On this diagram, we can go ahead
and identify line segment πΆπ· as here. From there, it might be helpful to
write out what we know based on this figure. We know that line segment π΅πΈ is
equal to line segment πΈπΆ. We also know that line segment π΅πΉ
is equal to line segment πΉπ΄. We know that line segment π΅π·,
π΄πΈ, and πΆπΉ all intersect at one point. And we know the measure of line
segment π΄πΆ is 13.8 centimeters.
What can we say based on this
information? Because the point πΈ divides line
π΅πΆ 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΄πΈ is a median. For that same reason, point πΉ is a
midpoint, and so we can say line segment πΆπΉ is a median because π΄πΈ and πΆπΉ 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·πΆ.
Then we know to find the value of
line segment πΆπ·, 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
πΆπ· has a length of 6.9 centimeters.
