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.
