Parallel & perpendicular lines

identify all sets of parallel and perpendicular lines in the image below so let's start with the parallel lines and just as a remember just as a reminder two lines are parallel if they're in the same plane and all of these lines are clearly in the same plane they're in the plane of the screen you're viewing right now but there are two lines that are in the same plane that never intersect and one way to verify because you can sometimes it looks like two lines won't intersect but you can't just always assume based on how it looks you really have to have some information given in the diagram or the problem that tells you that they are definitely parallel that they're definitely never going to intersect and one of those pieces of information which they give right over here is that they show that line st and line u v they both intersect line CD at the exact same angle at this angle right here and in particular it's at a right angle and if you have two lines that intersect a third line at the same angle at the same angle so these are actually called corresponding angles and they're the same if you have two of these corresponding angles the same then these two lines are parallel so line st is parallel to line u v and we can write it like this line st line st we put the arrows on each end of that top bar to say that this is a line not just a line segment line st is parallel to line to line u v and i think that's the only set of parallel lines in this diagram yep now let's think about well now let's think about perpendicular lines perpendicular lines are lines that intersect our R it lines that intersect at a 90 degree angle so for example line st is perpendicular line CD so line st is perpendicular to line CD and we know that they intersect at a right angle or a 90 degree angle because they gave us this little box here which loading means that the measure of this angle is 90 degrees by the exact same argument line U V is perpendicular to CD so UV let me make sure I specify these as lines line UV is per radicular to CD so I did you V St the perpendicular CD and then after that the only other information where they definitely tell us that two lines are intersecting at right angles our line a B and WX so a B a B is definitely perpendicular to W to W X line WX and I think we are done and a one thing to think about a B and C D those are definitely not well they don't even intersect in this diagram so you can't make any comment about perpendicular but they're definitely not parallel you could even imagine that they looks like they're about to intersect and they give us no information that they intersect the same lines at the same angle so if somehow they told us that this is a right angle even though it doesn't look anything like a right angle then we would have to suspend our judgment based on how it actually looks and say oh I guess maybe those things are maybe those things are perpendicular and then actually it actually or maybe these two things are parallel but they didn't tell us that and that would actually be bizarre as it looks so not parallel and actually you would have then this would end up being parallel to other things as well if that was done but and it's good thing that wasn't because it would look very strange but get based on the information they gave us these are the parallel and the perpendicular lines