Understand Points, Lines, Rays, Segments & Angles in Geometry - [7] - Free Educational videos for Students in K-12

Understand Points, Lines, Rays, Segments & Angles in Geometry - [7] - By Math and Science

Transcript


00:00	Hello . Welcome back . The title of this lesson
00:02	is called points , lines , rays , segments and
00:07	angles . This is part one . You might say
00:09	. That's a lot of different concepts . Why are
00:11	we covering them all in one place ? Well we're
00:13	starting to talk a little more seriously about geometry .
00:16	And so it makes sense to put all these together
00:18	because they are very closely related . So before we
00:20	get started let's just talk big picture geometry is all
00:24	around us . We really use it all the time
00:26	. Anytime you build a house or a bridge or
00:29	construct anything , you're using geometry . Even when you
00:32	launch spaceships or talk about like physics in terms of
00:35	gravity and all kinds of things . We use geometry
00:38	constantly to calculate things . So here we're starting the
00:42	very first steps on that journey . So we have
00:45	to talk about these terms and so we have lots
00:47	of figures and diagrams and we're gonna learn about what
00:49	these are . The first one is very simple .
00:51	A point . What is a point ? What does
00:53	it mean to you ? A point is a place
00:56	in space . That's what it means . A point
00:58	doesn't have any with it doesn't it's not fat or
01:01	skinny or anything . It's just a place in space
01:03	. If you can get a tiny microscopic needle and
01:06	point in one location , that would be the closest
01:08	thing to a point . It's just a location ,
01:10	right ? Everything else in geometry is built upon the
01:13	concept of a point . So let's start by talking
01:16	about the point , what a line is , what
01:18	array is and so on . So let's start talking
01:20	about it by looking at an actual diagram . So
01:23	here we have a point B . The point is
01:26	represented in geometry by a dot right ? We have
01:29	a point A . And we have a point C
01:32	. Now these are obviously joined together by these arrows
01:36	, so notice though that the arrow is only on
01:38	one side . And over here , there's no arrow
01:40	over here , there's an arrow on one side ,
01:42	but there's no arrow here . So if you cover
01:45	up this half of the diagram and just look at
01:47	what's going on over here . This thing here from
01:50	B to C is called a ray array is just
01:53	like what you think of a ray of light ,
01:55	It shoots out from one place and it goes on
01:57	and on forever . So this ray going from B
02:00	to C , starts at B , and it goes
02:02	on and on and ever through the point C .
02:04	Going this way , and the arrow means it goes
02:06	forever . The rate does not go forever . This
02:09	way it starts at point B . So this ray
02:12	is called B , C . And the way that
02:14	we write it and we know it's a ray is
02:15	because we put an arrow on the top . That
02:17	means it only goes one way from B to C
02:20	. And it starts from B . And it goes
02:22	through see forever . Now we have another ray on
02:24	this diagram , it starts at B . And it
02:27	travels through the point and goes on and on forever
02:30	. So this ray is called B . A .
02:32	Notice . The first letter you put is where the
02:34	starting point is , and then the arrow travels over
02:37	the other point it goes through . So be A
02:39	. Goes this way Bc goes this way , we
02:42	would talk about the ray B . A . We
02:44	would talk about the ray B . C . We
02:47	would talk about the point A . To point B
02:50	. The point C . But the ray has to
02:53	have at least two points . It has to go
02:55	somewhere . So we have to have two letters to
02:57	form array , one starting point , and then it
02:59	goes through uh the other the other point as well
03:03	. All right . Now we have another word that
03:05	we have used in the past . We call it
03:07	the vertex . So we have this angle here and
03:10	the angle is measured uh As the kind of the
03:13	how much spread is between this ray and this ray
03:18	. An angle can be measured between lines are between
03:21	raise when they come to a common point like this
03:23	. This is the angle measure like this . How
03:25	do we write names of angles ? Well , the
03:28	middle letter here is called the vertex . So the
03:31	vertex is B . And when we write down the
03:33	angle the vertex B must be in the middle .
03:35	So we call this angle A . B . C
03:39	. We could also I don't have it on the
03:40	page here , but we can also name it angle
03:42	C . B . A . It doesn't matter which
03:45	way you right the angle name down , but you
03:48	do have to have the middle point here . The
03:50	vertex in the middle . That's how we always name
03:52	angle . So you can call it angle abc .
03:55	This little symbol , the little slant thing is called
03:58	the angle symbol . So this means angle abc .
04:01	You can also call it angle C . B A
04:04	, Ray B A . Goes this way ray B
04:07	C . Goes this way vertex . The vertex just
04:10	means the center of the angle where the to raise
04:12	come together . That's what vertex is a vertex is
04:14	a corner , essentially vertex is basically a corner .
04:18	So we've talked about these concepts . Now let's move
04:20	on to the next diagram . We have we can
04:22	talk about some other concepts here . We talked about
04:25	the concept of a point . We've talked about the
04:27	concept of an angle . We talked about the vertex
04:30	, which is the center of the angle where the
04:32	to raise come together . Now we're going to talk
04:34	about angles again , let's see how many angles do
04:37	we have here in this rectangle here notice we have
04:40	a 90 degree angle symbol here . This symbol means
04:43	90 degrees , 90 degrees , 90 degrees . To
04:46	form a rectangle . You have to have 4 90
04:48	degree angles . That's what a rectangle is , right
04:51	? So we know that we have these angles and
04:53	they're 90 degrees . How would we name this angle
04:56	right here ? The angle measure ? How would we
04:58	name it ? Well , the angle is measured from
05:01	here to here . So the way we name it
05:03	is the same way we did hear A . B
05:05	. C . The vertex has to be in the
05:07	center , X . Is the vertex . We're gonna
05:09	name it W . X . Y . This is
05:13	going to tell us this is the angle we're talking
05:15	about W X . Y . This angle measure because
05:18	the X vertex is in the center . Now ,
05:21	we could also call it angle Y X W .
05:24	That's fine too , because it doesn't matter the way
05:27	that you you name the angles , you just have
05:29	to have the vertex , the corner of the angle
05:32	in the middle , that's all that matters Now ,
05:35	vertex we said was X . For this angle Now
05:38	we have to talk about the concept of a line
05:41	segment . A line segment is exactly what it says
05:44	. A line goes on and on and on forever
05:46	. If I point a line in this way ,
05:49	then the line is really going in both directions with
05:52	a double headed arrow forever . For the end of
05:55	the universe . A line never , ever , ever
05:58	stops , array goes forever ever . But remember array
06:02	starts at a point , but a line doesn't start
06:05	at one location . A line goes both directions forever
06:07	, ever , ever . Right ? But a line
06:10	segment is when you take a line and you cut
06:12	it and you say , well , I only have
06:13	a segment of that line . So , for instance
06:16	, take a look at this right here . This
06:18	is a line segment because it is a straight line
06:20	. But of course it's not going forever . It
06:22	starts at W and an N . X . This
06:24	is a line segment . This is a line segment
06:27	. This is a line segment . Why are these
06:29	not raise ? Because a ray remember goes on and
06:32	on and on . This arrow means it goes on
06:34	and on and on forever . But a segment does
06:36	not do that , A segment stops . So this
06:39	is a line segment . This is a line segment
06:41	. This is a line segment . This is a
06:42	line segment . Now , How do we name them
06:44	? Just like you might think this line segment is
06:47	named W . X . W . X . With
06:49	a bar on the top . Or you can flip
06:52	it around and call it X W . X .
06:54	W with a bar on the top . This means
06:56	either name is okay when you're naming a line segment
06:59	, what about this line segment ? We can call
07:01	it line segment Xy . Which means we put X
07:04	. Y . With a bar on top . Or
07:06	we can call it a line segment Y . X
07:08	. With a bar on top . So when you're
07:10	naming segments , it doesn't matter the order in which
07:13	you write the letters because , well , it just
07:16	doesn't really matter because it's it's a like a mirror
07:18	image . It doesn't matter what side you talk .
07:20	Neither side is more important than the other . Neither
07:23	endpoint is more important . But with a ray notice
07:26	the ray , we have to start at the point
07:27	B and call it ray , B , C .
07:29	Or be A . Because B . Is the starting
07:32	point of the ray and the rate goes on and
07:35	on forever in the other direction . So we have
07:37	to name it in the right way here for a
07:39	segment . We just use the letters and put a
07:41	bar on top . Notice there is no arrow in
07:43	this bar because it is not a ray , it
07:46	doesn't go forever , it stops . So a line
07:48	segment has a bar on top . A ray has
07:51	an arrow on top and that is a really important
07:53	difference . So before we solve our problems , which
07:56	are all going to be very simple , I promise
07:57	you , let's review a point is just a location
08:01	in space . You could say , this is point
08:03	W Point Y point Z point C point B Point
08:08	A . Those are all called points . Then we
08:11	have something called rays , which are just when we
08:13	start at a point and we go on and on
08:15	forever in one direction , this is a ray .
08:17	This is a ray . We call it ray B
08:19	. A . This way ray , B C .
08:21	This way we start at the vertex of the starting
08:24	point and we go right , we can have instead
08:28	of array , we can have segments , line segments
08:31	, right ? Where we don't have an arrow ,
08:33	but we know that we're going between W and X
08:36	. And it's a line segment . So we put
08:37	the letters and stick a bar on top X .
08:40	Y . Same thing . Just put the letters ,
08:41	put a bar on top no arrowheads because we just
08:44	have a segment , right ? Then we can of
08:46	course form angles with our line segment , W X
08:50	, Y , Y , X W . For instance
08:52	, we can also form angles with raise A .
08:54	B , C or C . B . A .
08:57	The symbol for an angle is a kind of a
08:59	slanted kind of like a little angle symbol , like
09:01	a mouth here and the same symbol right here .
09:05	And then of course we have the concept of a
09:06	line which I didn't draw on the board , but
09:08	a line is when it goes on and on and
09:10	on and on and on and on and on both
09:11	directions , never stopping in either direction . So now
09:15	that we have all of that , we finally know
09:17	enough to solve a couple of problems . Here is
09:21	an angle . We have some points here . This
09:23	is the vertex of the angle and we want to
09:25	answer a couple of questions . The first question is
09:28	, what are the to raise in this angle ?
09:30	How do we write down the to raise well the
09:33	rays that we have ? We see an arrow here
09:36	. So we have a ray going up like this
09:37	and we have an arrowhead here which means a ray
09:40	going off like this . The other side is not
09:42	an arrowhead so it does not go on and on
09:45	this way it starts at you and it goes through
09:48	V . And it starts at you and it goes
09:50	through T . So we have to raise here ,
09:52	what are they called ? We call them ray U
09:55	. V . And we put an arrow head this
09:58	direction and we put a comma here and we call
10:01	ray U . T . With an arrow head this
10:04	direction . This is how we write it . You
10:06	ve and you T . The U . Comes first
10:09	because that's the starting point . And then we have
10:11	the second point you ve . And then you T
10:13	. And the arrowhead points from U . To V
10:15	. Points from you to T . So it tells
10:18	us how the diagrams laid out just by writing the
10:20	name down . All right . The second question is
10:22	, what is the vertex of this angle here ?
10:24	The vertex is just a corner which is the kind
10:26	of the inside kind of the middle point where the
10:29	to raise joined up . So the vertex is just
10:32	the point . You that's just a point in space
10:35	. Now , how do we name this angle ?
10:38	You can name it actually two ways but we're gonna
10:40	name it for this location . We're gonna call it
10:42	angle T U v T u V . Right now
10:47	you could name it angle V U T V U
10:52	T . So T u v v ut same exact
10:55	thing . Notice you is in the center in both
10:57	cases so either of these names is fine for the
11:00	angle . Um But going forward , I'm just gonna
11:03	write one name down . So I'm not gonna write
11:05	every single name . You can name these things in
11:07	multiple ways . So let me take these off the
11:09	board . We're gonna solve some more problems to give
11:10	you more practice . All right . Welcome back to
11:13	problem too . We have this triangle here and each
11:17	of the points are we call vert vert is is
11:20	the plural of vertex's verte asi . We label them
11:23	J . H . And I . And we want
11:25	to ask ourselves a few questions . This is the
11:27	angle that we're talking about here with the red arc
11:29	right here . The first question is , what are
11:31	the segments the line segments that make up this angle
11:34	here on the board ? So in other words ,
11:36	we have an angle here . What segments form this
11:38	angle ? Well , they're joined together here . So
11:40	it's this line segment and it's also this line segment
11:43	. So we have to write these segments down .
11:44	There's multiple ways that you can name this . But
11:47	I'm gonna call this segment J . H . We're
11:50	gonna put a line segment symbol over J . H
11:53	. And we're gonna call this segment , we're gonna
11:55	have to call it something here , We're gonna call
11:57	it H . I . H . I . Now
12:02	I just want you to realize that when you name
12:04	these line segments you can you can flip the order
12:06	of the letters right ? Because it doesn't there's no
12:08	arrow here . There's no preference to what corner makes
12:12	more sense . In other words , this is J
12:13	. H . We could call it H . J
12:15	. With a bar on top . This one is
12:17	H . I . But I could call it I
12:19	. H . With a bar on top and it
12:21	would mean the same thing . All right . Next
12:24	question . What is the vertex of this angle with
12:26	? The vertex is just the point where the segments
12:29	come together . So the vertex is just the point
12:31	H . Very simple . And then the next question
12:34	is the last question here , what is the name
12:36	of this angle ? How do we name this angle
12:38	now ? There's a couple of different ways I'm gonna
12:40	call it angle J . H I . J .
12:44	H . I Now I'm trying to emphasize that there's
12:47	more than one way to write this . The angle
12:48	could be called I H . J . But H
12:52	has to be in the center . All right .
12:54	So that was problem number two . Let's take a
12:56	look now at problem number three . Now we have
12:59	a regular old angle here that is formed from this
13:02	ray and this raid we know that they're raised because
13:05	they have arrowheads . Okay . And so the first
13:08	question is , what are the rays that form this
13:11	angle ? What are the names of the rays ?
13:12	Well this ray starts at point Q . And it
13:15	goes through point are so we have to call this
13:18	rake you are . And the arrowhead goes like this
13:22	. What is the other ray starts at point ?
13:24	Q . Goes through point P . Q . P
13:28	arrowhead like this . And we have to use these
13:30	names . We cannot flip them around because for a
13:32	ray there is a starting point and then it goes
13:35	on forever . The starting point is Q . So
13:37	Q comes first Q . R . And then QP
13:40	. For the segments we can flip the names of
13:43	the letters because there's no arrowhead anywhere . But for
13:45	these there's an arrowhead . So there is a starting
13:47	point . That's why we have to write this Q
13:49	. R . In QP . What is the vertex
13:51	of this angle ? The vertex are where the rays
13:53	come together , vertex is essentially the corner . And
13:56	so the vertex is the point . Q . How
13:58	do we name this angle ? Well there's multiple different
14:01	ways to name it . But we're gonna call it
14:03	P Q r P q r Q has to be
14:08	in the center bonus points if you can tell me
14:11	another name of this angle . Well , instead of
14:13	P Q R we can call it R . Q
14:15	. P as long as Q is in the center
14:17	, you can name angles multiple ways . Alright PQ
14:21	Our next problem we have what appears to be a
14:24	square . It looks like the length of these signs
14:27	are all the same but maybe they're not quite .
14:28	But anyway we have four right angles so we know
14:31	for sure it's a rectangle and it might be a
14:33	square if we have the lengths of the sides all
14:35	the same . So the question is for this guy
14:38	, what are the names of the line segments that
14:41	make up the angle X . Down here , Right
14:43	. This angle here that we're looking at one of
14:45	the segments that make that up . Well here is
14:49	a segment here and here's a segment here . These
14:51	are the two segments that make this angle . So
14:53	we're gonna call it segment W . X . With
14:56	a line segment bar . And we're gonna call it
14:58	segment Xy Now because these are line segments , we
15:04	can flip the order instead of W . X .
15:06	We could call it a line segment X . W
15:08	. Instead of X . Y . We could call
15:10	it line segment Y . X . Because there's a
15:13	bar on top and there's no arrowhead . Then we
15:15	can flip the order of the letters if you want
15:17	to . All right , what is the vertex of
15:20	this angle ? Of course . It's what these two
15:22	segments are joined at point X . So the vertex
15:24	is point X . And how do we name this
15:26	angle here is the angle it goes from W .
15:29	X . Y . So we're gonna call it angle
15:31	symbol W . X . Y . Now , of
15:35	course , bonus points . If you tell me the
15:36	other angle , it could be called angle Y .
15:38	X . W . That's fine too . I'm not
15:41	gonna write every name for every one of these guys
15:43	, but that is the idea . Mhm . Alright
15:47	, next problem . We have a nice angle formed
15:50	here at point F . And we have a ray
15:52	going through G . And we have a race starting
15:54	at F . And going through E . So what
15:56	are the to raise ? We've already kind of said
15:58	the rays all started F . And this one goes
16:01	through G . So we have an arrowhead on top
16:05	and then we have another ray that starts with F
16:07	. And it goes through E . Now for the
16:10	rays you cannot flip the order of the letters because
16:12	they have a starting point F . And so you
16:14	have to put the arrow on top and you have
16:16	to start at F . Like we have done here
16:18	. What is the vertex of this angle ? It's
16:20	where the to raise come together , it's point F
16:24	. And the angle here . How would I name
16:25	it ? The angle . There's two ways to name
16:28	the angle we're gonna call it . E F G
16:31	E F G . You can also name this angle
16:35	angle G F . E . So E F G
16:39	R G F E . Same thing . Alright ,
16:42	last problem in this lesson here , we have a
16:46	12345 segment figure here . Or five sided figure here
16:50	. What are the segments that make up ? The
16:53	angle over here is indicated by the arrow . This
16:55	is angle M . With the vertex of em here
16:58	. So what segments do we have ? We have
16:59	this segment and we have this segment . How do
17:01	we name this ? Well we can name it different
17:03	ways but this segment goes from L . Two M
17:06	. So we're gonna call it segment L . M
17:10	. And then we have also a segment from M
17:12	. Going to end . So we're gonna call it
17:14	segment M . N . Notice there is no arrowhead
17:17	on top because this is a segment . These are
17:19	segments not raise . We call it L . M
17:22	. We could call it segment M . L .
17:24	This is M . N . We could call this
17:26	segment in M . So we can flip the order
17:29	of the letters if we want . When we're naming
17:30	the segments , what is the vertex of this angle
17:33	? It's where the segments come together ? The vertex's
17:36	point . M that's just a point . And then
17:39	how do you name this angle ? What is the
17:40	name of this angle ? And there's a couple of
17:42	ways to do it . We're gonna call it L
17:43	. M . N . So we're gonna call it
17:46	angle L . M N angle LMN . But of
17:51	course , you know by now that you can also
17:53	name it N . N . L . As long
17:55	as M is in the center , which it is
17:58	. So we actually covered a lot of material in
18:00	this lesson . And I hope now you can see
18:02	why we lumped it all together because we talk about
18:05	points but we have to understand what the point is
18:07	in order to talk about a ray because a race
18:09	starts at a point and it goes through another point
18:12	, right ? And then we have to talk about
18:14	line segments and those can be used to form angles
18:17	and so on . So we have to kind of
18:18	talk about it all together . We would like you
18:21	to do is go back through this lesson , draw
18:23	these figures herself and try to name the different things
18:25	that we named in this lesson . Even if you
18:27	just saw it , that's okay . I want you
18:28	to get practice and when you feel like you understand
18:31	what's happening , Follow me on the part two ,
18:32	we'll give you a little more practice to wrap up
18:34	the concept understanding points , lines , rays , angles
18:38	and vertex is

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