What I want to do in this

video is give an introduction to the language or

some of the characters that we use when we

talk about geometry. And I guess the

best place to start is even think about

what geometry means, as you might recognize the

first part of geometry right over here. You have the root word

geo– the same word that you see in things

like geography and geology. And this refers to the Earth. My E looked like a C right over. This refers to the Earth. And then you see

this metry part. And you see metry in

things like trigonometry as well and metry or

the metric system. And this comes from

measurement or measure. So when someone’s talking

about geometry, the word itself comes from

Earth measurement. And that’s not so bad

of a name, because it is such a general subject. Geometry really is

the study and trying to understand how shapes and

space and things that we see relate to each other. So when you start

learning about geometry, you learn about lines and

triangles and circles. And you learn about angles. And we’ll define all of

these things more and more precisely as we go

further and further on. But it also encapsulates

things like patterns and three-dimensional shapes. So it’s almost

everything that we see. All of the visually mathematical

things that we understand can in some way be

categorized in geometry. Now, with that out of

the way, let’s just start from the basics, a basic

starting point from geometry. And then we can just

grow from there. So if we just start at a dot,

that dot right over there, it’s just that little point on

that screen right over there. We literally call that a point. And I’ll call that a definition. And the fun thing

about mathematics is that you can

make definitions. We could have called

this an armadillo. But we decided to call this

a point, which, I think, makes sense, because it’s

what we would call it in just everyday

language as well. That is a point. Now, what’s interesting

about a point is that it is just a position. You can’t move on a point. If you were at this point and

if you moved in any direction at all, you would no

longer be at that point. So you cannot move on a point. Now, there are differences

between points. For example, that’s

one point there. Maybe I have another

point over here. And then I have

another point over here and then another

point over there. And you want to be able to

refer to the different points. And not everyone has the

luxury of a nice colored pen like I do. Otherwise, they could

refer to the green point or the blue point

or the pink point. And so in geometry

to refer to points, we tend to give them labels. And the labels tend

to have letters. So for example, this

could be point A. This could be point B.

This would be point C. And this right over

here could be point D. So someone says,

hey, circle point C. You know which one to circle. You know that you would

have to circle that point right over there. Well, that so far is

kind of interesting. You have these

things called points. You really can’t move

around on a point. All they do is

specify a position. What if we want to move

around a little bit more? What if we want to get

from one point to another? So what if we

started at one point and we wanted all of the points,

including that point, that connect that point at

another point, so all of these points right over here. So what would we call this

thing, all of the points that connect A and

B along a straight– and I’ll use everyday

language here– along a straight line like this? Well, we’ll call

this a line segment. In everyday language,

you might call it a line. But we’ll call it

a line segment, because we’ll see when we

talk in mathematical terms a line means something

slightly different. So this is a line segment. And if we were to

connect D and C, this would also be

another line segment. A line segment. And once again,

because we always don’t have the luxury

of colors, this one is clearly the

orange line segment. This is clearly the

yellow line segment. We want to have the labels

for these line segments. And the best way to

label the line segments is with its end points. And that’s another word here. So a point is just

literally A or B. But A and B are also the end

points of these line segments, because it starts and ends at

A and B. So let me write this. A and B are end points, another

definition right over here. Once again, we could

have called them aardvarks or end armadillos. But we, as

mathematicians, decided to call them end

points, because that seems to be a good name for it. And once again, we need a way to

label these line segments that have the end points. And what’s a better way

to label a line segment than with its actual end points? So we would refer to this

line segment over here, we would put its

end points there. And to show that

it’s a line segment, we would draw a line

over it just like that. This line segment down here,

we would write it like this. And we could have just as

easily written it like this. CD with a line over it would’ve

referred to that same line segment. BA with a line over it would

refer to that same line segment. Now, you might be saying,

well, I’m not satisfied just traveling in between A and B. And this is actually

another interesting idea. When you were just on A,

when you were just on a point and you couldn’t

travel at all, you couldn’t travel in any

direction without staying on that point, that means you

have zero options to travel in. You can’t go up or down, left

or right, in or out of the page and still be on that point. And so that’s why we say a

point has zero dimensions. Zero dimensions. Now, all of a sudden,

we have this thing, this line segment here. And this line segment

we can at least go to the left and the right

all along this line segment. We can go towards

A or towards B. So we can go back or

forward in one dimension. So the line segment is a

one-dimensional idea almost or a one-dimensional object. Although these are

more abstract ideas. There is no such thing as

a perfect line segment, because you can’t move up

or down on this line segment while being on it, while in

reality, anything that we think is a line segment, even a

stick of some type, a very straight stick or a

string that is taut, that still will have some width. But the geometrical pure

line segment has no width. It only has a length here. So you can only

move along the line. And that’s what we say

it’s one-dimensional. A point you can’t move at all. A line segment you can only

move in that back and forth along that same direction. Now, I just hinted that it

can actually have a length. How do you refer to that? Well, you refer to that by

not writing that line on it. So if I write AB with a

line on top of it like, that means I’m referring

to the actual line segment. Let me do this in a new color. If I say that AB is equal to 5

units– it might be centimeters or meters or whatever, just

the abstract units 5– that means that the distance

between A and B is 5, that the length of line

segment AB is, actually, 5. Now, let’s keep on extending it. Let’s say we want to just

keep going in one direction. So let’s say that I start at A. Let me do this in a new color. Let’s say I start at A.

And I want to go to D. But I want the option

to keep on going. So I can’t go further

in A’s direction than A. But I can go further

in D’s direction. So this little idea that I

just showed, essentially, it’s like a line

segment, but I can keep on going past this

endpoint, we call this a ray. And the starting point for a

ray is called the vertex, not a term that you’ll

see too often. You’ll see vertex later

on in other contexts. But it’s good to know. This is the vertex of the ray. It’s not the vertex

of this line segment. So maybe I shouldn’t

label it just like that. And what’s interesting

about a ray is it’s once again a

one-dimensional figure. But you can keep on going

past one of the endpoints. And the way that we

would specify a ray is we would call it AD. And we would put this little

arrow over on top of it to show that it is a ray. And in this case,

it matters the order that we put the letters in. If I put DA as a ray, this

would mean a different ray. That would mean that

we’re starting at D. And then we’re going past

A. So this is not ray DA. This is ray AD. Now, the last idea that I’m

sure you’re thinking about is, well, what if I could keep

on going in both directions? So let’s say I could keep going. My diagram is getting messy. So let me introduce

some more points. So let’s say I have

point E. And then I have point F right over here. And let’s say that I

have this object that goes through both E

and F but just keeps on going in both directions. When we talk in geometry terms,

this is what we call a line. Now, notice a line never ends. You can keep going

in either direction. A line segment does end. It has end points. A line does not. And actually, a line

segment can sometimes be called just a segment. And so you would specify line

EF with these arrows just like that. Now, the thing that you’re

going to see most typically when we’re studying geometry

are these right over here, because we’re going to

be concerned with sides of shapes, distances

between points. And when you’re talking about

any of those things, things that have finite

length, things that have an actual length, things

that don’t go off forever in one or two

directions, then you are talking about a

segment or a line segment. Now, just to keep

talking about new words that you might confront

in geometry, if we go back talking about a line,

I was drawing a ray. So let’s say I have

point X and point Y. And so this is line segment XY. So I could denote

it just like that. If I have another

point, let’s say I have another point

right over here. Let’s call that point Z. And

I’ll introduce another word. X, Y, and Z all lie

on the same line, if you would imagine

that a line could keep going on and

on forever and ever. So we can say that X,

Y, and Z are collinear. So those three

points are collinear. They all sit on the same line. And they also all sit

on line segment XY. Now, let’s say we’re told

that XZ is equal to ZY and they are all collinear. So that means this is telling

us that the distance between X and Z is the same as the

distance between Z and Y. So sometimes we can

mark it like that. This distance is the same

as that distance over there. So that tells us that

Z is exactly halfway between X and Y. So

in this situation, we would call Z the

midpoint of line segment XY, because it’s exactly

halfway between. Now, to finish up, we’ve

talked about things that have zero

dimensions– points. We’ve talked about things that

have one dimension– a line, a line segment, or a ray. You might say, well,

what has two dimensions? Well, in order to

have two dimensions, that means I can go

backwards and forwards in two different directions. So this page right

here or this video or this screen that

you’re looking at is a two-dimensional object. I can go right-left. That is one dimension. Or I could go up-down. And so this surface of the

monitor you’re looking at is actually two dimensions. You can go backwards or

forwards in two directions. And things that

are two dimensions, we call them planar. Or we call them planes. So if you took a piece of

paper that extended forever, it just extended in

every direction forever, that in the geometrical

sense was a plane. The piece of paper

itself, the thing that’s finite– and

you’ll never see this talked about in a

typical geometry class. But I guess if we were

to draw the analogy, you could call a piece of

paper maybe a plane segment, because it’s a segment

of an entire plane. If you had a third

dimension, then you’re talking about our

three-dimensional space. In three-dimensional

space, not only could you move left to right along

the screen or up and down, you could also move in

and out of the screen. You also have this dimension

that I’ll try to draw. You could go into the screen. Or you could go out of

the screen like that. And as we go into higher

and higher mathematics, although it becomes

very hard to visualize, you’ll see that

we can even start to study things that have

more than three dimensions.

I'm going to high school next year and i was watching this video and taking notes so it would help me. I thought geometry would be hard but this looks so easy. Thank you so much!

My teacher is always talking about school, why go to school if you can, watch it here😊😉

Thank-you

Khan academy makes math really boring but they make learning math a lot easier

watching these vids help me prepare for the next grade

they should have called the point an armadillo 🙁

i dont need to go to school this is my teacher

6:19 😂😂😂😂 still awesome vid helpful too 👏👏👏👏

This just refreshed everything I learned about geometry in Grade School. Crazy what you can get down in a 13 minute YouTube video…

Why am I here I was searching simple geometry hanzo

Haha jokes on my teacher I'm gonna be ahead thank you😂

thanks khan academy

thanks khan academy

so helpfull man im a freshman in geometry can u imagine how hard it is but just the 4th day of school thanks for this explination guys if you havent already hit the like button and sub

Any definitions for direction?

Yeah but Hanzo is better at geometry

This is perfect! I love how he explained each step thumbs up!!! 👍🏻❤️

Go subscribe to my channel plz

I love this academy! Much appreciate for Mr. Khan <3

10:50

7:21

uh uh uh uh uh uh uh a stick !

Your voice is deep

6:20

Thanks you so much!!

My teacher gives a new concept everyday and expects people to understand. In 45 minutes it’s not enough time to learn completely in a class but thanks to this guy I’m able to learn concepts so thank you

Simple geometry.

HAVING MY MAP TEST TOMMOROW MATH

At school I am failing geometry at the moment because my teacher does not know how to teach !

his voice is so boring but very interesting and useful for my school

a a a a stick 6:20

Im at grade 3 and there teaching us that

Geo

Some of the some of the some of the😞i hate math

All my life, I've never studied Geometry; not even in high school. In nz for me, every math study was different. So that's why I want to understand Geometry more and hope I can learn fast.

Thanks for help in my exam

I started 7th grade and I was very confused about everything, now after watching these videos I feel a hundred times more confident, thank you for making such great videos 😁.

It's a dot not a point

thank you for this video, it will help me a

lot

Khan academy I’m studying for my asvab and I’m wondering if the basics in algebra and geometry are in Algebra 1 and high school geometry basically can I jump right into these subjects and it will still cover the basics without doing pre algebra or basic geometry I just don’t want to waste time and cover the same thing twice

god dam your better than my teacher

This is the first time I ever understood geometry and I am 50!. I wish I had you for a math teacher when I was in school. Lol lol 😂

You Sound Like Mr. Nightmare

My mom is forcing me to watch this

amazing

0:04 Some of the, Sum of the, SUMM OV THI.!!!

pin me

Geometry – what's the point?

What is he using for this video?

Who's here one day before exam

Geometry is definitely one of those areas that gets all of us confused at times. Has anyone had problems with Pythagoras Theorem calculations?

6:20 lol

What did the triangle say to the ball?

You're pointless.

how do you get the coler pen

Thank You.🤗

Geometry! Ge, ge, ge, Geometry, khan always repeating to emphasize a point. Nevertheless, maybe annoying or not. But is a well executed technique. hahah

I don't like my math teacher I have two math classes and in one class I have all As but in my other class I have all C,D and F but in both of my math classes we are doing the same stuff my math teacher that I am Failing with is Mrs.Rivers nobody like here she is a bad teacher.My math teacher that I have all A in is Mrs.Dear what do you suggest I should do??? It's like I am in two different classes but Mrs.Rivers is the most annoying teacher in the world.

I simply suck at math. 🙂 failing yay!

I’ve always loved KhanAcademy I always used it at school

Teacher: Okay kids, so this line segments has two aardvarks, one at each end of the line segment.

Student: Why are they called aardvarks?

Teacher: Because I like Khan Academy and I really don’t care anymore

This is good learning

thank the lord for this

im in 6th grade and im doing geometry…. UGHHHHHHH

1:48 this video has a point.

But if point is 0 dimension and line is made up of adding many points then how could line be 1 dimension ( since 0+0+0+0…=0) ??

This seems a lot easier then algerbra

thank you for introducing this video, I want to learn about this cuz MTAP (math) its our learning competition of math.

#YOUCANLEARNANYTHING

Geo > Earth

metry> measurement

Geometry > Earth-measurement

Why point why not dot

Thank you for this video. Pass my test bc of it

I'm about to go to 8th and I'm in gt math where we are gonna learn geometry and I'm lost

some of the some of the. s o m e o f t h eWhen youtube is better than my own teacher

THIS HELPED ME SOOOO MUCH MY TEACHER IS SO BORING AND SLOW HE EXPECTS US TO UNDERSTAND THAAANKKK YOUUUUU

Thanks10000 times🌻

Hanzo likes this.

Watching yall's geometry videos cuz my geo teacher doesn't speak goog english

How does this help me 10 years from now

Line goes on and on and on forever

There is no forever

some of the some of the

yeet

Beet

just saying geometry is probably the most pointless concept I've ever learned

top lel

lol my education fails me

I'm in 4th grade and I'm doing it ughhh

Armmadilos

uh uh uh uh uh

Make Russian subtitles!!!

Perfect I am studying for a test

1:53 We could have called this an armadillo 😂

I died from laughing

Also me: I'm not dead if you don’t get puns

a a a a a a a a a a -1 hour later a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a a stick You Can Find This Part At 2:60 And There’s no hour part 😃

So when will your average hs student use geometry a day in their life?

The world of science is fascinating. Imagine the world 300 years back then where the society only starts developing and yet, some of the brightest minds invented these formulas that even now, are still useful in our modern world. They are so powerful that revolutionized the world. I love where this is going. Never going to stop learning even after college.

About to take my say in August hope this is helping lol

This really be a bruh moment

khan is my new teacher

Is geometry easier than algebra…..I just started 9th and I’m in geometry and all the people in my class are 10th and 11th graders and I’m kinda scared that I chose the wrong class. I need reassurance

He sounds like vlad Lyubovny!