### Video Transcript

Using the information in the
figure, determine the length of line segment πΈπΉ.

First of all, we can identify line
segment πΈπΉ. And then we need to think about
what we know based on the figure. In the figure, we have three
parallel lines. Line π΄π· is parallel to line πΈπ΅,
which is parallel to line πΉπΆ. We can also say that lines π·πΉ and
π΄πΆ are transversals of the three parallel lines. Based on this, we know that the
parallel lines are going to cut the transversals proportionally. This means that line segment π·πΈ
over line segment π΄π΅ will be equal to line segment πΈπΉ over line segment π΅πΆ
because of the parallel lines and transversal properties. Once we have this statement, we can
just plug in the values for the three line segments we know and use that information
to solve for the fourth line segment, which will look like this. 48 over 47 is equal to πΈπΉ over
141.

From there, we cross multiply. 141 times 48 must be equal to 47
times πΈπΉ. 6768 is equal to 47 πΈπΉ. And then we divide both sides of
this equation by 47, which tells us that 144 is equal to πΈπΉ. And so we can say that line segment
πΈπΉ must measure 144 centimeters.