# Angle basics | Angles and intersecting lines | Geometry | Khan Academy

– Let’s say we have one ray

over here that starts at point A and then goes through point B, and so we could call this ray– let me draw that a little bit straighter, we could call this ray AB, ray AB starts at A or has a vertex at A and let’s say that there’s also a ray AC, so let’s say that C is

sitting right over there and then I can draw another

ray, goes through C, so this is ray AC. What’s interesting about these two rays is that they have the exact same vertex, they have the exact same vertex at A. In general, what we have

when we have two rays that have the exact same

vertex, you have an angle and you’re probably already

reasonably familiar with the concept of an angle, which I believe comes from

the Latin for “corner”, which makes sense, this looks

like a little bit of a corner right over here that we see at point A and the geometric definition, or the one that you’re most likely to see, is when two rays share a common vertex and that common vertex is actually called the vertex of the angle, so A is vertex. Not only is it the vertex

of each of these rays, ray AB and ray AC, it is also the vertex of the angle. The next thing I want to think

about is how do we label? How do we label an angle? You might be tempted to

just label it angle A but I’ll show you in a second

why that’s not going to be so clear to someone based on where our angle is actually sitting. The way that you specify an angle, and hopefully this will

make sense in a second, is that you say “angle”, this is the symbol for angle and it actually looks

strangely similar to this angle right over here, but

this little pointy thing or it almost looks like a less-than sign but it’s not quite, it’s flat

on the bottom right over here. This is the symbol for angle, you’d say angle BAC or you could say angle CAB. In either case, they’re kind of specifying this corner, or sometimes

you could view it as this opening right over here. The important thing to

realize is that you have the vertex in the middle of the letters. You might be saying, “Wait,

why go through the trouble “of listing all three of these letters? “Why can’t I just call this angle A?” To see that, let me show

you another diagram. Although the geometric

definition of an angle involves two rays that

have the same vertex, in practice, you’re

going to see many angles that are made up of

lines and line segments. You could imagine that you could continue those line segments on

and on in one direction and then they would become rays so, in that way, they’re

consistent this definition. Let’s add one line segment

that looks like that, let me label some points here, so we’ve already used ABC

so let me call this D and E, points D and E, so this

is line segment DE. Let’s say I also have line segment FG, FG, and let’s say this point where these two line segments intersect, let’s called that point, point H. How could we specify this

angle right over here? Can we just that angle H? Well, no, because if we just said angle H, the angle that has a vertex H, it could be this angle right over here or it could be this angle right over here, let me draw it this way, you could view it that way or it could be that angle over there, it could be this angle over here, it could be this angle over here or it could be that angle over there and so the only way to really specify which angle you’re talking about well is to give three letters. If you really did want

to talk about that angle right over there, you

would call that angle EHG, so that is angle EHG or you could actually specify that or you could call that angle GHE. GHE If you wanted to specify

this angle right over here, if you wanted to specify

that angle right over here, the one made up of, if

you imagine that ray and that ray, if you were to keep on going past those points, then you

could call that angle DHG angle DHG, or angle GHD, or angle GHD, I think you get the point. This angle up here could be FHE or EHF and this one could be FHD or DHF and when you do it this

way, it’s very clear what angle you are referring to. Now that we have a general

idea of what an angle is and how do we denote it with symbols, the next thing you might

be curious about is, it doesn’t look like

all angles are the same, it seems like some angles open up or are more open than others and some are a little bit

more closed in than others and that actually is the case. For example, let’s take two angles here, let’s say I have one angle

that looks like that, so I’ll start reusing letters, so let’s say that this is A, B and C, I can make these rays,

I could keep on going and make them rays if I like or I could just keep

them as line segments, so right over here I have angle BAC and let’s say over here, I have angle– so let me draw another one, and let’s say this is angle XYZ and, once again, I could

draw them as rays if I like, to go on and on and on, so it’s angle X, Y and Z. When you just look at these, you just eyeball these two angles, it looks like this one is more open, so this one looks more open while this one over

here looks more closed, so it looks like it’s more closed, at least relative to

this one, more closed. Maybe when we measure angles, we should measure it based on

how open or closed they are and that actually is the case, and so without even telling

you how we measure an angle, you could say that the

measure of angle XYZ, the measure of this angle is greater than the measure

of this angle right over here and any convention we

use for measuring angles is essentially going to be a measure of how open or how closed

an angle actually is and I’ll take that up in the next video where we’ll see how to

actually measure an angle.

yay angles (=

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Great courses! Getting a geometry refresher course.

This helped me with my class. Thank you! I'm in 9th grade Geometry (high school).

if i only could download your brain data in to my brain.

i have also a ray in my pants

How are there 45,702 views and only 9 comments?

im trying to get ahead in geometry for when i start high school, so these videos are absolutely perfect for me. thanks mr khan! 😀

Thank You for the great videos. This will absolutely helps me in school.

These videos help so much! Thank you!

Helped me in school 😃

People usually view it at khanacademy[dot]org, so most of the comments and questions goes to the "forum" (section comment, or whatever you wanna call it) that each video has under it, and it works well, since most of the frequently doubts of most people are in the top 3 Q&As.

How do u write with that? What did u do?

This is a great step in math for me im in the 4th grade

I,m rawww

Bro. I need this be4 going into geometry. Im just searching up all the geometry videos i could find.

I love math I hope I get a math teacher

Since i was 2nd year high school at the age of 9, i remember this video learning advance geometry lesson. Sounds Classic.

nice

Is there a video on finding angle between two lines in cartesian c.s.?

Interesting

My math teacher told us to search up angle vids 📐

SHUT THE FUCK UP KHAN

THIS MAKES NO SENSE!!!!!!!!

Nice

Nice

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Good

I got confused on what comes first a b or c do I need a dictionary

helped me in my geometry class! thx so much! SUBBED!!

I was so confused thanked for teaching me

which english it is American or British

You are our savior Sal! Keep up the best work.

thanks i think tis is so confused but no this is so easy thanks .

Who watches this in 2017

nice !!!!

Boy

We watch ur videos for math class….when my math teacher is there showing us ur videos instead of her teaching lol

this is so useful

so im here because im in second year i dont know what its there in america maybe 9th grade or something. But I got into a crappy math class because of my bad grades on exam so im really really trying now to learn geometry before we really get into it in school so ik the jist of whats going on. thankfully khan academy exists in my era.

This is helping me More than i thought

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Did they ever learn how to hold shift to make actual straight lines? Or does Khan Academy not have a keyboard in their setup? Ir maybe it's a style thing?

But yeah, in almost All competent drawing software you will wither have a line tool or the ability to hold shift and drag (mouse or stylus.) Most drawing programs with shape tools tend to make this the key bind for keeping dimensions for transforms.

I know for sure Smoothdraw has it, well not sure if it was a feature in 2011 though. Sadly no circle tool, it's a neat scribble pad though.

5:41 bac and cab

2018?

This is so helpful

Nice job and keep it up

this is a great video thanks

soooooooooo boring

JazakAllah so much!💖

This is actually relatively easy it’s just my teacher sucks

you are a very good teacher

Math is easy. Its just the teachers. Smh. I could do alot better if these teachers would actually teach like Khan

Funny how this one video taught me more in 6 minutes than my geometry 1 class taught me in an entire week

Thank you for the clarity of angels it helps

Hi khan academy i recommend that you make the videos more interesting like math antics that would be a good update

nice

ya my math teacher is also showing your videoes instead of teaching

EASY Thanks Sal even though you are a bit confusing in ur other vids u explained i well so i subbed

You explain angles very very well

I was to lazy to go to the Khan Academy website so I went to YouTube.

Also, the uppercase letter A is an angle

we could call this ray, we could call, let me draw that a little bit straighter, we could call this ray AB, ray AB

I breath math

I live math

I need Kahn academy to survive

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Can we say angle ABC

hi thanx