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If lines π΄π΅ β«½ πΆπ· β«½ πΈπΉ and πΆπΈ = 2 cm, find π΄πΈ.

If lines π΄π΅, πΆπ·, and πΈπΉ are all parallel and πΆπΈ equals two centimeters, find π΄πΈ.

We can see in the diagram that we are given three parallel lines and two transversals. We can also see that π΅π· is equal to π·πΉ. So, in this case, the parallel lines divide one of the transversals into line segments of equal length. We can recall that 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. Therefore, it will divide the other transversal into sections of equal length. Thus, π΄πΆ is equal to πΆπΈ, which is equal to two centimeters. We note that π΄πΈ is equal to π΄πΆ plus πΆπΈ. So π΄πΈ is equal to two centimeters plus two centimeters, which equals four centimeters.

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