Video transcript
Identify all sets ofparallel and perpendicular lines in the image below. So let's start withthe parallel lines. And just as areminder, two lines are parallel if they'rein the same plane, and all of these lines areclearly in the same plane. They're in theplane of the screen you're viewing right now. But they are two lines thatare in the same plane that never intersect. And one way to verify,because you can sometimes-- it looks like twolines won't intersect, but you can't just alwaysassume based on how it looks. You really have tohave some information given in the diagram orthe problem that tells you that they aredefinitely parallel, that they're definitelynever going to intersect. And one of thosepieces of information which they giveright over here is that they show thatline ST and line UV, they both intersect lineCD at the exact same angle, at this angle right here. And in particular,it's at a right angle. And if you have two linesthat intersect a third line at the same angle--so these are actually called corresponding anglesand they're the same-- if you have two of thesecorresponding angles the same, then these twolines are parallel. So line ST isparallel to line UV. And we can write it like this. Line ST, we put the arrowson each end of that top bar to say that this is a line,not just a line segment. Line ST is parallel to line UV. And I think that's theonly set of parallel lines in this diagram. Yep. Now let's think aboutperpendicular lines. Perpendicular linesare lines that intersect at a 90-degree angle. So, for example, line ST isperpendicular to line CD. So line ST isperpendicular to line CD. And we know that theyintersect at a right angle or at a 90-degree anglebecause they gave us this little box herewhich literally means that the measure of thisangle is 90 degrees. By the exact same argument, linethe UV is perpendicular to CD. Let me make sure Ispecified these as lines. Line UV is perpendicular to CD. So I did UV, ST, they'reperpendicular to CD. And then after that, theonly other information where they definitely tell usthat two lines are intersecting at right anglesare line AB and WX. So AB is definitelyperpendicular to WX, line WX. And I think we are done. And one thing to thinkabout, AB and CD, well, they don't evenintersect in this diagram. So you can't make anycomment about perpendicular, but they're definitelynot parallel. You could evenimagine that it looks like they're about to intersect. And they give us noinformation that they intersect the same lines atthe same angle. So if somehow they told us thatthis is a right angle, even though it doesn't lookanything like a right angle, then we would have tosuspend our judgment based on how it actuallylooks and say, oh, I guess maybe thosethings are perpendicular, or maybe these twothings are parallel. But they didn't tell us that. And that wouldactually be bizarre because it looksso not parallel. And actually thenthis would end up being parallel to other thingsas well if that was done. It's a good thingthat wasn't because it would look very strange. But based on theinformation they gave us, these are the parallel andthe perpendicular lines.
