Video Transcript
In the given figure, the line
between 𝑋 and 𝐴 is parallel to the line between 𝑌 and 𝐵 is parallel to the line
between 𝑍 and 𝐶 is parallel to the line between 𝐿 and 𝐷. And the line between 𝑋 and 𝐿 and
the line between 𝐴 and 𝐷 are two transversals. If 𝑋𝑍 is equal to 11 centimeters,
then 𝑋𝐿 is equal to what centimeters.
In this question, we are given a
pair of transversals of four parallel lines in a diagram and asked to use this to
determine the length of a line segment of one of the transversals between a pair of
the parallel lines. To do this, we are given that line
segment 𝑋𝑍 has length 11 centimeters, and we can also note in the diagram that the
parallel lines divide the transversal 𝐴𝐷 into segments of equal lengths. This can remind us of the result
that if any set of parallel lines divides a transversal into segments of equal
length, then those same parallel lines must divide any transversal into segments of
equal lengths.
Therefore, since the set of
parallel lines divides transversal 𝐴𝐷 into segments of equal length, they also
divide the transversal 𝑋𝐿 into segments of equal length. In particular, we have 𝑋𝑌 equals
𝑌𝑍 equals 𝑍𝐿.
We can then note that line segment
𝑋𝑍 is formed from two line segments of equal length, and its total length is 11
centimeters. So each section of the transversal
𝑋𝐿 has length 11 over two centimeters, which is 5.5 centimeters.
Finally, we see that line segment
𝑋𝐿 is formed from three of these segments. So 𝑋𝐿 is equal to three times 5.5
centimeters, which is equal to 16.5 centimeters.
