Angle Basics

Definition of an angle. How to denote an angle using points on the angle (including the vertex)

Lets 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 (we could call, 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 lets say that there is also a ray AC. So lets say that C is sitting

right over there and then i can draw another ray that goes through C, so this is ray AC. and what's interesting

about these two rays is that they have the exact same vertex. (they have the exact same vertex at A)

and in general what we have when we have two rays with the exact same vertex, you have an angle. and

you've probably, 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 a little bit like a corner right over

here that we see at point A and, but the geometric definition, or the one you are more 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, of the angle. so 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, where our angle is actually sitting. so 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 almost looks like a less than sign, but it's not quite. its flat on the bottom right over here.

this is the symbol for angle, you would say angle BAC, BAC, or you could say angle CAB, or angle CAB.

and either case there kind of specifying this corner, or sometimes you could view it as this opening

right over here. and the important thing to realize is that you have the vertex in the middle of the

letters. and you might be saying why go through the trouble of listing all three of these letters, why

can't i just call this angle A. and to see that, let me show you another diagram. and although the geometric

definition involves, two rays that have the same vertex

in practice, you are going to see many angles

made of line and line segments

Lets say I have one line segment like that, let me

label it DE, and lets also have line segment, FG

and lets say the point where the two line segments interact

is H, how could we specify this angle right over here

can we call it as angle H, if we say it as angle H,

it could be this angle, that angle or this angle over here

it could be this angle over here. The only way to specify

which can we are talking about is to give 3 letters

if you want to talk about this angle, you will call it

angle EHG, or could call it angle GHE,

if you wanted this angle over here, you could call it

angle DHG, or angle GHD. i think you get the point.

this angle is angle FHE or EHF and this is angle FHD or

DHF. now are are clear which angle you are referring to.

So now we have a general idea what an angle is and how

we denote it with symbols, it does not look like

all angles look the same. Some are more open than others

So for example, let us take two angles here,

angle BAC, and let's say over here, I have angle XYZ

when you look at these angle XYZ is more open

while this angle is more closed, compared to the other angle

when we measure angles, we must measure it on how open

or closed they are. The measure of angle XYZ, is greater

than the measure of the angle ABC.

Any measure of angles, is based on how open, or closed

they are which we will see in the next vidoes