# Two straight lines are shown prove that the never meet again

### Parallel & perpendicular lines | Basic geometry (video) | Khan Academy In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane Parallel planes are planes in the same three-dimensional space that never meet. Given parallel straight lines l and m in Euclidean space, the following a proof of the fact that if one transversal meets a pair of lines in congruent. It is easy, 1. Take a point on anyone line, draw perpendicular to other line and find the distance Now take another point, again draw a. Back to main course page To produce a finite straight line continuously in a straight line. That means that we never run out of space; that is, space is infinite . the two straight lines, if produced indefinitely, meet on that side on which are We knew the geometry of space with certainty and Euclid had revealed it to us.

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.

## Parallel & perpendicular lines

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.

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? So what is this thing right over here? This is actually a lot of fun. So once again, we're gonna have three students attempting to define, but now they're going to define "an object called an angle. Ruby says, "The amount of turn between two straight lines "that have a common vertex.

### Geometric definitions example (video) | Khan Academy

The definition of an angle, we typically talk about two rays with a common vertex. She's talking about two lines with a common vertex. And she's talking about the amount of turn. So she's really talk about more of, kind of, the measure of an angle. So let's see what comment here.

So, "You seem to be getting at the idea "of the measure of an angle, and "not the definition of the angle itself. I would put this one right here. We just got lucky. This was already aligned. The definition of an angle is two rays with a common vertex. So, "Two lines that come together," this is just intersecting lines.

## Parallel lines from equation (example 2)

Now, when that happens, you might be forming some angles, but I would just say, "Were you thinking of intersecting lines?

That's a good definition of an angle. So Abhishek got it this time. Let's do another one. So three students are now attempting to define "what it means for two lines to be parallel. So Daniela says, "Two lines are parallel "if they are distinct and one can be translated "on top of the other. So that actually seems pretty interesting. That's actually not the first way that I would have defined parallel lines. I would have said, "Hey, if they're on the same plane "and they don't intersect, then they are parallel.

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And so, if you're translating one If you can trans- If they're two different lines, but you can shift them without changing their direction, which is what translation is all about, on top of each other, that actually feels pretty good. So, I'll put that right over there. So Ori says, "Two lines are parallel "if they are close together but don't intersect.