Question Video: Finding the Lengths of Proportional Line Segments between Parallel Lines | Nagwa Question Video: Finding the Lengths of Proportional Line Segments between Parallel Lines | Nagwa

# Question Video: Finding the Lengths of Proportional Line Segments between Parallel Lines Mathematics • First Year of Preparatory School

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Given that ππΏ = 9 cm, find the length of line segment ππ.

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### Video Transcript

Given that ππΏ equals nine centimeters, find the length of line segment ππ.

The first thing we can note is that the four lines π΄π, π΅π, πΆπ, and π·πΏ are all marked as parallel on the diagram. We also have three congruent line segments shown. So π΄π΅, π΅πΆ, and πΆπ· are all equal in length. We are given the information that the line segment ππΏ is nine centimeters long. And we need to determine the length of line segment ππ.

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 ππΏ into congruent line segments such that ππ equals ππ equals ππΏ. 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 ππ and ππ of three and three centimeters each would give us the answer that the length of line segment ππ is six centimeters.

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