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# Angles: introduction

CCSS.Math:

## Video transcript

let's say we have one Rea over here that starts at Point a and then goes through point B and so we could call this R a we could call let me draw that a little bit straighter we could call this R a a be Ray a B 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 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 that have 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 like a little bit of a corner right over here that we see at Point a and but the 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 Ray's ray a B 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 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 BAC or you could say angle C a B or angle C a B in either case they're 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 now 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 and to see that let me show you another diagram and although the geometric definition of an angle involves 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 and 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 with this definition but let's say I have one line segment that looks like that now you 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 and let's say I also have line segments let's say I also have line segment FG f G and let's say this point where these two line segments inter intersect let's call that point point H now how could we specify how could we specify this angle right over here can we just call that angle H well no because angle 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 this 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 so let's so if you if you really did want to talk about if you really did want to talk about that angle right over there you would call that angle E H G so that is angle E H G or you could actually specify that or you could call that angle G H E G H E 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 way if you were to keep on going past those points then you could call that angle DHG angle DHG or angle GHD or angle G HD I think you get the point this angle up here could be F H e or e H F and this one could be FH D or D H F and when you do it this way you're very it's very clear what angle you are referring to so now we have a general idea of what an angle is and kind of how do we how do we denote it with with symbols the next thing you might be curious about it is it doesn't look like all angles are kind of 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 so for example let's take two - two angles here so let's say I have one angle that looks like that so let me I'll start reusing letters so let's say that this is a B and C I could make these rays I could keep on going and make them raised if I like or I could just keep them as line segments so right over here I have angle B AC and let's say over here I have angle so let me draw another one and let's say this is angle X Y angle XYZ and once again I could keep I could draw them is raised if I like to go on and on and on so it's angle x y and z and so 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 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 more closed so maybe when we measure angles we should measure it based on how open or close 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 year 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