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Lets say we have one ray over here that starts at point A and then goes through point B, and so we could

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call this ray (we could call, let me draw that a little bit straighter) we could call this ray AB. Ray AB

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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

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

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

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

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you've probably, you're probably already reasonably familiar with the concept of an angle which i believe

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comes from the latin for corner, which makes sense this looks a little bit like a corner right over

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here that we see at point A and, but the geometric definition, or the one you are more likely to see

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is when two rays share a common vertex. and that common vertex is actually called the vertex of the angle.

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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

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of, of the angle. so the next thing i want to think about is how do we label, how do we label an angle

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you might be tempted to just label it angle A, but i'll show you in a second why that's not going to

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be so clear to someone based on where, where our angle is actually sitting. so the way that you specify

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an angle, and hopefully this will make sense in a second, is that you say ANGLE, (this is the symbol

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for angle) and it actually looks strangely similar to this angle right over here, but this little pointy

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thing almost looks like a less than sign, but it's not quite. its flat on the bottom right over here.

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

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

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

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

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

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definition involves, two rays that have the same vertex

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in practice, you are going to see many angles

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made of line and line segments

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

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

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and lets say the point where the two line segments interact

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

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

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

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

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which can we are talking about is to give 3 letters

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

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angle EHG, or could call it angle GHE,

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

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

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

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

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

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we denote it with symbols, it does not look like

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

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So for example, let us take two angles here,

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

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when you look at these angle XYZ is more open

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

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

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

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than the measure of the angle ABC.

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

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they are which we will see in the next vidoes