[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.27,0:00:08.80,Default,,0000,0000,0000,,Lets say we have one ray over here that starts at point A and then goes through point B, and so we could
Dialogue: 0,0:00:09.47,0:00:12.93,Default,,0000,0000,0000,,call this ray (we could call, let me draw that a little bit straighter) we could call this ray AB. Ray AB
Dialogue: 0,0:00:16.33,0:00:18.87,Default,,0000,0000,0000,,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
Dialogue: 0,0:00:21.33,0:00:25.60,Default,,0000,0000,0000,,right over there and then i can draw another ray that goes through C, so this is ray AC. and what's interesting
Dialogue: 0,0:00:32.20,0:00:35.73,Default,,0000,0000,0000,,about these two rays is that they have the exact same vertex. (they have the exact same vertex at A)
Dialogue: 0,0:00:40.47,0:00:43.60,Default,,0000,0000,0000,,and in general what we have when we have two rays with the exact same vertex, you have an angle. and
Dialogue: 0,0:00:47.47,0:00:50.60,Default,,0000,0000,0000,,you've probably, you're probably already reasonably familiar with the concept of an angle which i believe
Dialogue: 0,0:00:53.13,0:00:55.80,Default,,0000,0000,0000,,comes from the latin for corner, which makes sense this looks a little bit like a corner right over
Dialogue: 0,0:00:58.20,0:01:00.60,Default,,0000,0000,0000,,here that we see at point A and, but the geometric definition, or the one you are more likely to see
Dialogue: 0,0:01:04.27,0:01:07.67,Default,,0000,0000,0000,,is when two rays share a common vertex. and that common vertex is actually called the vertex of the angle.
Dialogue: 0,0:01:12.67,0:01:16.53,Default,,0000,0000,0000,,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
Dialogue: 0,0:01:19.93,0:01:24.67,Default,,0000,0000,0000,,of, of the angle. so the next thing i want to think about is how do we label, how do we label an angle
Dialogue: 0,0:01:28.47,0:01:31.33,Default,,0000,0000,0000,,you might be tempted to just label it angle A, but i'll show you in a second why that's not going to
Dialogue: 0,0:01:35.60,0:01:39.80,Default,,0000,0000,0000,,be so clear to someone based on where, where our angle is actually sitting. so the way that you specify
Dialogue: 0,0:01:42.27,0:01:46.60,Default,,0000,0000,0000,,an angle, and hopefully this will make sense in a second, is that you say ANGLE, (this is the symbol
Dialogue: 0,0:01:52.73,0:01:58.20,Default,,0000,0000,0000,,for angle) and it actually looks strangely similar to this angle right over here, but this little pointy
Dialogue: 0,0:02:00.93,0:02:05.33,Default,,0000,0000,0000,,thing almost looks like a less than sign, but it's not quite. its flat on the bottom right over here.
Dialogue: 0,0:02:07.80,0:02:09.80,Default,,0000,0000,0000,,this is the symbol for angle, you would say angle BAC, BAC, or you could say angle CAB, or angle CAB.
Dialogue: 0,0:02:10.60,0:02:13.13,Default,,0000,0000,0000,,and either case there kind of specifying this corner, or sometimes you could view it as this opening
Dialogue: 0,0:02:15.47,0:02:16.93,Default,,0000,0000,0000,,right over here. and the important thing to realize is that you have the vertex in the middle of the
Dialogue: 0,0:02:19.87,0:02:21.47,Default,,0000,0000,0000,,letters. and you might be saying why go through the trouble of listing all three of these letters, why
Dialogue: 0,0:02:24.20,0:02:27.13,Default,,0000,0000,0000,,can't i just call this angle A. and to see that, let me show you another diagram. and although the geometric
Dialogue: 0,0:02:27.13,0:02:36.60,Default,,0000,0000,0000,,definition involves, two rays that have the same vertex
Dialogue: 0,0:02:36.60,0:02:39.67,Default,,0000,0000,0000,,in practice, you are going to see many angles
Dialogue: 0,0:02:39.67,0:02:50.47,Default,,0000,0000,0000,,made of line and line segments
Dialogue: 0,0:02:50.47,0:02:54.27,Default,,0000,0000,0000,,Lets say I have one line segment like that, let me
Dialogue: 0,0:02:54.27,0:03:07.80,Default,,0000,0000,0000,,label it DE, and lets also have line segment, FG
Dialogue: 0,0:03:07.80,0:03:15.00,Default,,0000,0000,0000,,and lets say the point where the two line segments interact
Dialogue: 0,0:03:15.00,0:03:20.53,Default,,0000,0000,0000,,is H, how could we specify this angle right over here
Dialogue: 0,0:03:20.53,0:03:27.80,Default,,0000,0000,0000,,can we call it as angle H, if we say it as angle H,
Dialogue: 0,0:03:27.80,0:03:45.00,Default,,0000,0000,0000,,it could be this angle, that angle or this angle over here
Dialogue: 0,0:03:45.00,0:03:49.47,Default,,0000,0000,0000,,it could be this angle over here. The only way to specify
Dialogue: 0,0:03:49.47,0:03:54.87,Default,,0000,0000,0000,,which can we are talking about is to give 3 letters
Dialogue: 0,0:03:54.87,0:04:01.47,Default,,0000,0000,0000,,if you want to talk about this angle, you will call it
Dialogue: 0,0:04:01.47,0:04:12.40,Default,,0000,0000,0000,,angle EHG, or could call it angle GHE,
Dialogue: 0,0:04:12.40,0:04:18.93,Default,,0000,0000,0000,,if you wanted this angle over here, you could call it
Dialogue: 0,0:04:18.93,0:04:40.87,Default,,0000,0000,0000,,angle DHG, or angle GHD. i think you get the point.
Dialogue: 0,0:04:40.87,0:04:45.60,Default,,0000,0000,0000,,this angle is angle FHE or EHF and this is angle FHD or
Dialogue: 0,0:04:45.60,0:04:54.53,Default,,0000,0000,0000,,DHF. now are are clear which angle you are referring to.
Dialogue: 0,0:04:54.53,0:04:58.47,Default,,0000,0000,0000,,So now we have a general idea what an angle is and how
Dialogue: 0,0:04:58.47,0:05:02.93,Default,,0000,0000,0000,,we denote it with symbols, it does not look like
Dialogue: 0,0:05:02.93,0:05:13.27,Default,,0000,0000,0000,,all angles look the same. Some are more open than others
Dialogue: 0,0:05:13.27,0:05:19.13,Default,,0000,0000,0000,,So for example, let us take two angles here,
Dialogue: 0,0:05:19.13,0:05:58.93,Default,,0000,0000,0000,,angle BAC, and let's say over here, I have angle XYZ
Dialogue: 0,0:05:58.93,0:06:06.33,Default,,0000,0000,0000,,when you look at these angle XYZ is more open
Dialogue: 0,0:06:06.33,0:06:15.80,Default,,0000,0000,0000,,while this angle is more closed, compared to the other angle
Dialogue: 0,0:06:15.80,0:06:22.27,Default,,0000,0000,0000,,when we measure angles, we must measure it on how open
Dialogue: 0,0:06:22.27,0:06:32.00,Default,,0000,0000,0000,,or closed they are. The measure of angle XYZ, is greater
Dialogue: 0,0:06:32.00,0:06:38.13,Default,,0000,0000,0000,,than the measure of the angle ABC.
Dialogue: 0,0:06:38.13,0:06:44.53,Default,,0000,0000,0000,,Any measure of angles, is based on how open, or closed
Dialogue: 0,0:06:44.53,9:59:59.99,Default,,0000,0000,0000,,they are which we will see in the next vidoes