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### Course: Geometry (all content) > Unit 1

Lesson 1: Lines, line segments, and rays# Lines, line segments, & rays

Learn the difference between lines, line segments, and rays. Created by Sal Khan.

## Want to join the conversation?

- would an infinite line and an infinite ray be equally long? That's my question.(746 votes)
- no, look at set theory as an example. if there is a set that extends infinitely to all the positive numbers, and then there is a set that extends infinitely in both directions, with negative numbers and positive numbers, they are not equal set, because even though both are infinite, you cannot match up each element os the positive set with each element of the negative set. In other words, for every centimeter of the ray, there would be twice as many centimeter of line, therefore the line is longer(75 votes)

- Is line EF and line FE the same?(31 votes)
- Yup!

When naming a line using just two points, order usually does not matter.(43 votes)

- Does anyone else remember a ray by think of a ray of sunshine, it starts at the sun can't get in so it goes out?(22 votes)
- yes. It's how I originally thought of it when I heard of it(7 votes)

- Are the lines of longitude and latitude really mathematical lines? They do not go on forever and neither are they line segments since they do not have a starting point or ending point...(12 votes)
- The Earth is considered an oblique spheroid (in other words an irregular sphere). So, the longitude and latitude lines aren't really circles as they are ellipses.(7 votes)

- What is the best way to get better at geometry or any other type of math?(8 votes)
- Practice. The more you work at answering these types of problems, the more your brain will become accustomed to them. You'll get faster and more accurate at solving math problems.(22 votes)

- How come lines have no thickness? Isn't it as thick as the line?(6 votes)
- When you draw a line it has thickness, but that is just a representation. The abstract idea of a line, however, does not have any thickness.(14 votes)

- Would two lines that are coincident (identical lines) have infinite intersection? I know that two distinct lines intersect at one or no points. But two coincident lines?(8 votes)
- Okay so lines can extend in two directions but outwards,

what if we want them to extend inwards and collapse at a point?(7 votes)- Lines don't collapse, at best they intersect. The point is that we can give a line 0, 1, or 2 endpoints.(8 votes)

- so a line is going on forever in two driections and a line segment goes on one driection right?(2 votes)
- A line segment doesn't go in any direction. It's just a small piece of a line, with two endpoints. You are thinking of a ray, which goes on forever in one direction.(10 votes)

- how do you do division?(3 votes)
- if you know how to do multiplication do that just basically reverse(6 votes)

## Video transcript

What I want to do
in this video is think about the difference
between a line segment, a line, and a ray. And this is the pure geometrical
versions of these things. And so, a line segment
is actually probably what most of us associate with
a line in our everyday lives. A line segment is
something just like that. For lack of a better
word, a straight line. But why we call it a
segment is that it actually has a starting and
a stopping point. So, most of the lines
that we experience in our everyday
reality are actually line segments when
we think of it from a pure geometrical
point of view. and I know I drew a little
bit of a curve here, but this is supposed to
be completely straight, but this is a line segment. The segment is based
on the fact that it has an ending point
and a starting point, or a starting point
and an ending point. A line, if you're
thinking about it in the pure geometric sense
of a line, is essentially, it does not stop. It doesn't have a starting
point and an ending point. It keeps going on forever
in both directions. So a line would look like this. And to show that it
keeps on going on forever in that direction right
over there, we draw this arrow, and to keep showing
that it goes on forever in kind of the down
left direction, we draw this arrow
right over here. So obviously, I've never
encountered something that just keeps on
going straight forever. But in math-- that's the
neat thing about math-- we can think about
these abstract notions. And so the mathematical purest
geometric sense of a line is this straight thing
that goes on forever. Now, a ray is
something in between. A ray has a well
defined starting point. So that's its starting
point, but then it just keeps on
going on forever. So the ray might
start over here, but then it just keeps on going. So that right over
there is a ray. Now, with that out of
the way, let's actually try to do the Khan
Academy module on recognizing the difference
between line segments, lines, and rays. And I think you'll find it
pretty straightforward based on our little classification
right over here. So, let me get the module going. Where did I put it? There you go. All right. So what is this thing
right over here? Well, it has two
arrows on both ends, so it's implying that
it goes on forever. So this is going to be a line. Let's check our answer. Yeah, it's a line. Now it's taking some time,
oh, correct, next question. All right, now what
about this thing? Well, once again,
arrows on both sides. It means that this
thing is going to go on forever
in both directions. So once again, it is a line. Fair enough. Let's do another one. Here we have one arrow,
so it goes on forever in this direction, but it has
a well-defined starting point. So it starts there, and
then goes on forever. And if you remember,
that's what a ray is. One starting point,
but goes on forever. Or one way to think
about it, goes on forever in only one direction. So that is a ray. So let's do another question. This right over here, you have
a starting point and an ending point, or you could call this
the start point and the ending point, but it doesn't go on
forever in either direction. So this right over
here is a line segment. There you go. So hopefully that gives
you enough to work your way through this module. And you might notice, when I
did this module right here, there is no video. And that's exactly
what this video is. It's the video for this module.