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## Basic geometry and measurement

### Course: Basic geometry and measurement > Unit 4

Lesson 3: Parallel and perpendicular# 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.

## Want to join the conversation?

- 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?(66 votes)- 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.(46 votes)

- Are perpendicular lines intersecting lines,but,intersecting lines not perpendicular lines?(20 votes)
- All perpendicular lines are intersecting lines , but not all intersecting lines are perpendicular lines.(18 votes)

- what are transversals? and how do I use them in Geometry(15 votes)
- Transversals are basically lines intersecting 2 or more lines. There may or may not be employments utilizing this skill, but nevertheless it is very important to learn this while in school (just for the exams at least :)).(21 votes)

- what is that symbol that looks like an upside-down capital T? Does it mean bisects or intercepts or perpendicular?(10 votes)
- The symbol ⊥ is the
**perpendicular sign**- it shows that two lines are perpendicular to each other.

For example:*line*AB ⊥*line*CD.

Hope this helps!(25 votes)

- Does it have to be a line? Can be line segments or rays?(15 votes)
- 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)

- what is the definition of a skew line?(10 votes)
- 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)

- Im having trouble remembering how a line is perpendicular. can someone tell me any tips or tricks for remembering?(6 votes)
- If you are having trouble remembering the difference between parallel and perpendicular lines, remember this: in the word "parallel", the two l's are parallel. Perpendicular lines are the opposite: the l's would make a 't' shape. That might help!(13 votes)

- soo it always at a 90 where it is prependicular? : )(8 votes)
- Actually, yes, lines that are perpendicular will always be at a 90 degree angle where they intersect.(8 votes)

- 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)
- Are you referring to what Sal was doing starting at0:39? 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.(7 votes)

- So perpendicular line are 90° angle?(9 votes)
- Correct. The angle between a line and its perpendicular is 90 degrees.(6 votes)

## 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.