Video Transcript
In triangle π½πΎπΏ, π½π equals six
centimeters. Find the length of line segment
ππ.
We need to know the length of line
segment ππ, and weβve been given that π½π equals six centimeters. First of all, we should note that
the point π divides the line segment πΎπΏ in half, which makes π a midpoint. Since π½ 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 π½π is a
median. In the same way, π divides line
segment π½πΏ and π
divides line segment π½πΎ, which means πΎπ is a median and πΏπ
is a median. Since π½π, πΎπ, and πΏπ
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 ππ will be equal to one-half the line segment π½π. Since π½π was equal to six
centimeters, we take one half of that and we say that the line segment ππ is equal
to three centimeters.
