Video Transcript
Given that 𝐴𝐷 equals six and 𝑍𝐿
equals 𝐶𝐷, find 𝑋𝑍 plus 𝑌𝐿.
If we look at the figure, we can
note that the four lines 𝐴𝑋, 𝐵𝑌, 𝐶𝑍, and 𝐷𝐿 are all marked as parallel. And we are given that the three
line segments 𝐴𝐵, 𝐵𝐶, and 𝐶𝐷 are marked as congruent. Therefore, we can say that the
transversal line 𝐴𝐷 has been split into congruent line segments by the four
parallel lines. And that also means we can apply an
important property here. It is 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.
And so, we can write that the line
segments 𝑋𝑌, 𝑌𝑍, and 𝑍𝐿 are all congruent. Notice, we are not saying that they
are all equal to the line segments in the transversal 𝐴𝐷 as well but simply that
they are equal in length to each other.
Now, we are given that the length
of the entire line segment 𝐴𝐷 is six length units. And as it is divided into three
congruent pieces, then each smaller line segment within it must be two units in
length. Next, we are also given that 𝑍𝐿
equals 𝐶𝐷. And so, both these line segments
are two units in length. And returning to the fact that all
the line segments on the transversal line 𝑋𝐿 are congruent, then the line segments
𝑋𝑌 and 𝑌𝑍 are also two length units.
Finally, we need to determine the
length of 𝑋𝑍 plus 𝑌𝐿. Line segment 𝑋𝑍 has a length of
two plus two length units. And line segment 𝑌𝐿 is also two
plus two length units. Adding these gives us the answer
that 𝑋𝑍 plus 𝑌𝐿 is eight. And if we needed a unit for the
answer, this would be length units.
