Math Antics - Points, Lines, & Planes - Free Educational videos for Students in K-12

Math Antics - Points, Lines, & Planes - By mathantics

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00:03	Uh huh . Hi there . Today on math Antics
00:08	were starting a new subject where we're going to learn
00:10	the basics of a special kind of math called geometry
00:13	. Geometry is the study of things like lines ,
00:16	shapes , angles , distances and things like that .
00:20	In this video , we're going to focus on three
00:22	of the most basic elements or parts of geometry .
00:26	There are points , Lines and planes . All right
00:30	. We're gonna start with points because they're about the
00:32	simplest thing you can imagine in geometry . What's the
00:35	point ? Well , let me draw some for you
00:39	. So these are points . They're just little tiny
00:42	dots in space . But they do a really important
00:45	job in geometry . They help us describe specific locations
00:48	in space , like the end of a line or
00:51	the corner of a square or the center of a
00:53	circle . Yeah , but they won't really help that
00:56	much unless we name them because if I say ,
00:58	hey , look at that point over there , it's
01:00	kind of hard to tell which one I'm talking about
01:02	. I mean they all look the same . Yeah
01:05	. So what name should we give these points ?
01:08	Well , let's see how about Archimedes and uh beauregard
01:14	, that'd be good . Um maybe charlemagne . How
01:17	about Daphne and Einstein ? Let's see fred and Guinevere
01:25	, Hiawatha and Ickarus . Perfect . You know ,
01:30	on second thought , those names are kind of long
01:32	and complicated . Why don't we just use the first
01:35	letters of each name instead there ? Now , if
01:39	I say look at point A or look at point
01:42	me , you know exactly what I'm talking about ?
01:45	Yeah . In fact , let's do that . Let's
01:47	just talk about point A and point B for a
01:50	minute . If you start at point A and go
01:52	to point B taking the shortest distance possible , you
01:55	would have gone in a straight line . A line
01:58	is the next most basic element of geometry . We
02:01	name a line by the points that it goes through
02:04	. For example , we would call this line A
02:06	. B . Because it's in points where it starts
02:09	and stops are points A . And B . But
02:12	technically this isn't really a line , it's a line
02:15	segment . What's the difference you ask ? That's a
02:18	good question . A line segment has a beginning and
02:21	an end it starts at one point in space and
02:24	it ends at another . A line on the other
02:26	hand just keeps on going in either direction forever .
02:30	Just like the number line keeps on going forever .
02:33	Well at least we imagine that it goes on forever
02:36	. We can't actually draw a line that goes on
02:38	forever . So here's what we do instead to draw
02:41	a line instead of a line segment , you just
02:44	go past the end points a little bit and you
02:46	put an arrow on both ends of the line to
02:48	show that it keeps on going . So this is
02:51	line segment A . B . And this is line
02:53	C . D . Now there's one more special type
02:56	of line that we need to talk about and it's
02:59	basically a combination of a line segment and the line
03:02	we call it a ray raise have beginning points ,
03:05	but no ending points . They just keep on going
03:08	forever , but only in one direction . So we
03:11	only put an arrow on the end that keeps going
03:13	there . We call this one Ray EF in geometry
03:19	. Each of these three types of lines has a
03:21	shorthand way of writing it . Instead of writing line
03:24	segment , maybe you can just write a B .
03:27	With a line over the top . And instead of
03:29	writing line C . D . You can write C
03:32	. D . With a double airline over them like
03:35	this . And finally instead of writing ray Ef ,
03:39	you can just write E . F . With a
03:41	single arrow line over them like . So okay so
03:45	now you know about points and you know that you
03:47	can form a lion between any two points . The
03:50	next thing we're going to learn about is planes .
03:52	No not the kind of planes that you fly now
03:56	to help you understand how planes and geometry work .
03:59	Let's go back and look at all those points that
04:01	we had at the beginning of the video . It
04:03	looks like all the points are the same depth on
04:05	your computer screen , right ? And if they were
04:07	would say that they're all in the same plane ,
04:09	that's because your computer screen is a plane . It's
04:12	a flat surface like a window or a sheet of
04:14	paper or a tabletop . A plane or flat surface
04:18	is what we call a two dimensional object because there's
04:21	two dimensions that you can move in . You can
04:23	go up and down . Or you can go left
04:25	and right . A line on the other hand is
04:28	a one dimensional object . If you're on a line
04:31	like line A . B . There's only one dimension
04:33	that you can travel in . Sure you can go
04:35	forwards or backwards along that line but it still has
04:38	only one dimension . You can't get to POINT C
04:41	. Without going off of lying . Maybe . But
04:44	if you're on a plane a two dimensional object then
04:47	you can get to Point C . Because Point C
04:49	. Is on the same plane as points A .
04:51	And B . All three of them are on that
04:53	flat two dimensional surface which is your computer screen .
04:57	Cool . So that means that if I want to
04:59	get to point D . I can do that too
05:01	because it's on the same plane as a B .
05:04	And C . Right ? All right . I have
05:06	a confession to make . I tricked you point the
05:09	really isn't in the same plane as the computer screen
05:12	. It just looks like it from the position you're
05:14	viewing it from . Watch what happens if I start
05:16	rotating the screen space a little bit ha . Now
05:20	you can see that the points are actually scattered all
05:23	over the place in space . Point D . Is
05:26	actually in front of the plane that A B and
05:28	C were in . Along with some of the other
05:30	points . And the rest of the points are actually
05:32	behind the plane that A B and C . Are
05:34	in . What we have here is a three dimensional
05:36	space or three D . Space for short , in
05:39	a three dimensional space , there's three dimensions . You
05:41	can move in left to right up and down and
05:45	in and out . If we're on the plane that
05:47	contains points A . B and C , we can't
05:50	get to point D . Unless we leave that plane
05:52	by traveling in that third dimension A three dimensional space
05:56	. Like this is often called the volume , but
05:59	we'll talk all about three D . Volumes in another
06:01	video . For now , let's get back to talking
06:03	about planes . Earlier in the video , we learned
06:06	that you can make a line by connecting any two
06:08	points . Right ? Well in order to make a
06:10	plane , it turns out that you need to have
06:12	three points Like our three points a B&C . If
06:16	you just connect A . And B . You get
06:18	a line . But if you connect A . B
06:20	. And C , you get a . A triangle
06:23	. Now you're probably thinking , wait , I thought
06:26	we were supposed to get a plane , not a
06:28	triangle . Well because it is a flat surface ,
06:31	a triangle is a lot like a plane But it
06:34	has three edges . It stops and doesn't keep on
06:37	going forever . When we were talking about lines .
06:40	Do you remember how a line segment had in points
06:42	? But a true line kept on going forever .
06:45	Well it's kind of the same way with triangles and
06:47	planes . You can think of a triangle as a
06:50	smaller part or a segment of a plane . But
06:52	the plane itself keeps on going forever . Yeah .
06:56	So three points is all it takes to define a
06:58	plane . And in the space we've been looking at
07:01	, we already have playing A . B . C
07:03	. So let's try making some other planes with the
07:05	rest of the points . We can choose any three
07:07	points that we want to . Let's join D .
07:10	E . N . F . Now we can see
07:11	the triangle they form . And if we extend that
07:14	flat triangle we can see the claim that it defines
07:17	. Let's try one more so the rest of the
07:19	points don't feel left out . Let's join G .
07:22	H . And I there they form this triangle ,
07:25	a flat surface that forms this plane . If we
07:28	extend it in every direction . So now , you
07:31	know about planes , lines and points . Three basic
07:34	elements of geometry . There's a lot more geometry ahead
07:37	in upcoming videos . So stay tuned and you can
07:41	check out the exercises for this section there pretty easy
07:44	and they'll help you remember what you've learned . Thanks
07:47	for watching . And I'll see you next time .
07:49	Learn more at math Antics dot com .

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