Question Video: Finding a Side Length Using Parallel Lines and Traversals Mathematics • First Year of Preparatory School

Video Transcript

If lines 𝐴𝐵, 𝐶𝐷, and 𝐸𝐹 are all parallel and 𝐶𝐸 equals two centimeters, find 𝐴𝐸.

We can see in the diagram that we are given three parallel lines and two transversals. We can also see that 𝐵𝐷 is equal to 𝐷𝐹. 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, 𝐴𝐶 is equal to 𝐶𝐸, which is equal to two centimeters. We note that 𝐴𝐸 is equal to 𝐴𝐶 plus 𝐶𝐸. So 𝐴𝐸 is equal to two centimeters plus two centimeters, which equals four centimeters.