# Question Video: Using the Properties of Parallel Lines to Solve a Problem Mathematics

Using the information in the figure, determine the length of πΈπΉ.

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### Video Transcript

Using the information in the figure, determine the length of line segment πΈπΉ.

First of all, we can identify line segment πΈπΉ. 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 πΈπ΅, which is parallel to line πΉπΆ. We can also say that lines π·πΉ and π΄πΆ 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·πΈ over line segment π΄π΅ will be equal to line segment πΈπΉ over line segment π΅πΆ 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 πΈπΉ over 141.

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