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Parallel & perpendicular lines

Parallel lines are lines that never intersect, and they form the same angle when they cross another line. Perpendicular lines intersect at a 90-degree angle, forming a square corner. We can identify these lines using angles and symbols in diagrams. Created by Sal Khan and Monterey Institute for Technology and Education.

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  • boggle yellow style avatar for user Joshua
    Are there parallel lines in reality? I mean, each time I draw parallel lines I'm doing my best to make them look like they would never intersect however you extend them on both of their ends, but I think because of many factors when I'm drawing parallel lines (e.g a little shaky hands, bumpy edge of the ruler, soft surface of the paper), the lines aren't really parallel, they will actually intersect at some point when you extend them.
    Do machines also have a very slight error when creating parallel lines?
    What about computers? Are they really good at processing graphics they are able to create perfectly parallel lines?
    Do parallel lines only exist in concept?
    (81 votes)
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    • duskpin ultimate style avatar for user CalebTheM
      Computers can because they have rows of pixels that are perfectly straight. It's not possible to draw two perfectly parallel lines, just as it isn't possible to draw a perfect circle. So yeah, parallel lines exist, but perfectly replicating them is pretty hard and can't be perfectly recreated by humans.
      (56 votes)
  • female robot ada style avatar for user rukayyatsallau
    Are perpendicular lines intersecting lines,but,intersecting lines not perpendicular lines?
    (24 votes)
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  • blobby green style avatar for user Bethany Smith
    what are transversals? and how do I use them in Geometry
    (17 votes)
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  • scuttlebug yellow style avatar for user valerie
    what is that symbol that looks like an upside-down capital T? Does it mean bisects or intercepts or perpendicular?
    (14 votes)
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  • aqualine ultimate style avatar for user Faith
    Does it have to be a line? Can be line segments or rays?
    (18 votes)
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    • aqualine ultimate style avatar for user Jace McCarthy
      Although I'm not exactly sure what you are asking I will explain how Lines, Line Segments, and Rays work. Lines are well lines and do not have any endpoints and are basically infinite. Line segments are like taking a piece of line. They have two endpoints and are not infinite. Last you have the ray which basically is like cutting a line in one spot but leaving one of the sides infinite. One endpoint and is infinite in one direction. Another thing to note is Parallel Lines/Parallel Rays/Parallel Line Segments. Basically they will never touch or get any farther or closer away. If you have other questions feel free to ask them.
      (10 votes)
  • cacteye purple style avatar for user nubia.1237210
    what is the definition of a skew line?
    (12 votes)
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    • cacteye green style avatar for user Hamza Usman
      The definition of a skew line is as follows:
      "In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel." It is important to note the part that says three-dimensional geometry because two lines cannot be skew lines in 2 dimensions. Skew lines are just lines that are in different planes that do not intersect, which fits the definition because two lines being parallel implies they are in the same plane.
      (12 votes)
  • starky seedling style avatar for user 28pmccanney
    Im having trouble remembering how a line is perpendicular. can someone tell me any tips or tricks for remembering?
    (7 votes)
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  • blobby green style avatar for user kaylakohutiak17
    soo it always at a 90 where it is prependicular? : )
    (9 votes)
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  • blobby green style avatar for user Kaz1000
    Couldn't one write that CD is perpendicular to ST and still be correct? This seems a more logical way of stating it, to me.
    (7 votes)
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    • hopper cool style avatar for user Artem Tsarevskiy
      Are you referring to what Sal was doing starting at ? You are correct that CD is perpendicular to ST, but at the moment Sal was demonstrating that ST is parallel to UV. He simply used CD as a transversal intersecting these two lines to prove that they are indeed parallel, and in the given illustration CD happened to intersect the lines at a 90 degree angle, making it perpendicular to UV and ST. Fundamentally, you are correct.
      (8 votes)
  • blobby green style avatar for user amibul8428
    So perpendicular line are 90° angle?
    (9 votes)
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Video transcript

Identify all sets of parallel and perpendicular lines in the image below. So let's start with the parallel lines. And 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 they 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 UV, 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-- 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 UV. And we can write it like this. 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 UV. And I think that's the only set of parallel lines in this diagram. Yep. Now let's think about perpendicular lines. Perpendicular lines are lines that intersect at a 90-degree angle. So, for example, line ST is perpendicular to line CD. So line ST is perpendicular to line CD. And we know that they intersect at a right angle or at a 90-degree angle because they gave us this little box here which literally means that the measure of this angle is 90 degrees. By the exact same argument, line the UV is perpendicular to CD. Let me make sure I specified these as lines. Line UV is perpendicular to CD. So I did UV, ST, they're perpendicular to CD. And then after that, the only other information where they definitely tell us that two lines are intersecting at right angles are line AB and WX. So AB is definitely perpendicular to WX, line WX. And I think we are done. And one thing to think about, AB and CD, 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 it 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 perpendicular, or maybe these two things are parallel. But they didn't tell us that. And that would actually be bizarre because it looks so not parallel. And actually then this would end up being parallel to other things as well if that was done. It's a good thing that wasn't because it would look very strange. But based on the information they gave us, these are the parallel and the perpendicular lines.