line point postulate definition geometry

But this isn't a good definition, because you can also have parallel lines that are far apart. That are close together and don't intersect on the same plane, and they are going to be parallel. It's, they just have to be in the same plane and not intersect. So Ori says, 'Two lines are parallel 'if they are close togetherīut don't intersect.' So, if you're trying toĭefine parallel lines, parallel lines, it doesn't matter if they're close together or not. If you can trans- If they're two different lines, but you can shift them withoutĬhanging their direction, which is what translation is all about, on top of each other, thatĪctually feels pretty good. Then they are parallel.' But this is, this seems pretty good because, if you're translating something, you're not, you aren't going to rotate it, you're not going to change its direction, I guess, one way to think about it. They're on the same plane 'and they don't intersect, That's actually not the first way that I would have defined parallel lines. So that actually seems pretty interesting. So Daniela says, 'Two lines are parallel 'if they are distinctĪnd one can be translated 'on top of the other.' All right. Lines to be parallel.' So now let's match the teacher's comments. Now attempting to define 'what it means for two Might be forming some angles, but I would just say, 'Were you thinking of intersecting lines?' And let's see what Abhishek says. So, 'Two lines that come together,' this is just intersecting lines.

Lines that come together.' So, once again, this is kind of. Of the angle itself.' So this is actually right. So, 'You seem to be getting at the idea 'of the measure of an angle, and 'not the definition

And she's talking aboutĪbout more of, kind of, the measure of an angle. We typically talk about two rays with a common vertex. Ruby says, 'The amount of turnīetween two straight lines 'that have a common vertex.' Well, this is kind of getting there. Now they're going to define 'an object called an angle.' 'Can you match the teacher'sĬomments to the definitions?' So Ruby, oh, it's three, Gonna have three students attempting to define, but Their point of intersection 'is a right angle,' is a 90 degree angle. They meet at one point 'and one of their angles at The teacher's comment, 'Yourĭefinition is kind of correct, 'but it lacks mathematical precision.' You know, what does he mean by a T? What does it mean to 'make a T'? Shriya's definition is much more precise. When you imagine perpendicular lines, you could imagine them kind of forming a cross or, I guess, part of. Abhishek says, 'l and m are perpendicular 'if they meet at a single point, 'such that the two lines make a 'T'.' Well, that's, in a hand-wavy I would say, 'Woohoo! Nice Work! 'I couldn't have said it better myself.' Now let's just make sure this comment matches for this definition. Their point of intersection 'is a right angle.' If the meet at one point 'and one of the angles at Plane and they never intersect, then you are talking about parallel lines. 'Were you thinking of parallel lines?' Because that's looks like So that is not going to be, that's not going to be correct. In fact, perpendicular linesįor sure will intersect.

M, 'are perpendicular 'if they never meet.' Well, that's not true. So Ruby's definitionįor being perpendicular: 'l and m,' lines l and It means to be perpendicular, and then there's these teacher's comments that we can move around. Three different students attempt definitions of what 'Can you match the teacher'sĬomments to the definitions?' All right. 'Three students attempt 'to define what it means for lines l and m 'to be perpendicular. And so, to get some practice being precise and exact with our language, I'm going to go through some exercises from the Geometric Definitions Exercise on Khan Academy. Things about the world, we have to be very careful, very precise, very exact with our language so that we know what we're proving and we know what we're assuming and what type of deductions we are making as we prove things. What geometry is about is proving things about the world.

Line point postulate definition geometry