### Video Transcript

Given that ππΏ equals nine
centimeters, find the length of line segment ππ.

The first thing we can note is that
the four lines π΄π, π΅π, πΆπ, and π·πΏ are all marked as parallel on the
diagram. We also have three congruent line
segments shown. So π΄π΅, π΅πΆ, and πΆπ· are all
equal in length. We are given the information that
the line segment ππΏ is nine centimeters long. And we need to determine the length
of line segment ππ.

Now, this may seem impossible,
until we recall that there is a property that we can apply here, which involves
parallel lines and transversals. If a set of parallel lines divide a
transversal into segments of equal length, then they divide any other transversal
into segments of equal length. So, because we do have the
transversal line π΄π· divided into congruent line segments by the four parallel
lines, then the same parallel lines also divide the other transversal line ππΏ into
congruent line segments such that ππ equals ππ equals ππΏ. And because these line segments are
all congruent and sum to nine centimeters, then they all must be three centimeters
each.

So, adding the lengths of line
segments ππ and ππ of three and three centimeters each would give us the answer
that the length of line segment ππ is six centimeters.