[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:02.10,0:00:05.30,Default,,0000,0000,0000,,Hello. In this series of presentations, I'm gonna try
Dialogue: 0,0:00:05.30,0:00:11.20,Default,,0000,0000,0000,,to teach you everything you need to know about triangles and angles and parallel lines
Dialogue: 0,0:00:11.20,0:00:18.80,Default,,0000,0000,0000,,and this is probably the highest-yield information that you could ever learn, especially in terms of the standardized tests.
Dialogue: 0,0:00:18.80,0:00:22.30,Default,,0000,0000,0000,,And then when we've learned all the rules we'll play something I call the Angle Game,
Dialogue: 0,0:00:22.30,0:00:25.60,Default,,0000,0000,0000,,which is essentially what the SAT makes you do over and over again.
Dialogue: 0,0:00:25.60,0:00:29.10,Default,,0000,0000,0000,,So let's start with some basics.You know what an angles is.
Dialogue: 0,0:00:29.10,0:00:35.30,Default,,0000,0000,0000,,Well actually maybe you don't know what an angle is.
Dialogue: 0,0:00:35.30,0:00:46.00,Default,,0000,0000,0000,,If I have two lines...
Dialogue: 0,0:00:46.00,0:00:48.80,Default,,0000,0000,0000,,and they intersect at some point,
Dialogue: 0,0:00:48.80,0:00:55.90,Default,,0000,0000,0000,,the angle is a measure of exactly how wide the intersection is between those two lines.
Dialogue: 0,0:00:55.90,0:01:05.50,Default,,0000,0000,0000,,So this is the angle. An angle is how wide those two lines open up.
Dialogue: 0,0:01:05.50,0:01:12.60,Default,,0000,0000,0000,,And they're measured either in degrees or radiants. And for the sake of most geometry classes we'll use degrees.
Dialogue: 0,0:01:12.60,0:01:16.30,Default,,0000,0000,0000,,When we start doing Trigonometry we'll use radiants.
Dialogue: 0,0:01:16.30,0:01:21.70,Default,,0000,0000,0000,,And you're probably familiar with this. Zero degrees would be two lines on top of each other...
Dialogue: 0,0:01:21.70,0:01:27.70,Default,,0000,0000,0000,,this if I were to just eyeball it looks like 45 degrees.
Dialogue: 0,0:01:27.70,0:01:38.80,Default,,0000,0000,0000,,If I had the lines even wider apart, like that, that's 90 degrees.
Dialogue: 0,0:01:38.80,0:01:41.40,Default,,0000,0000,0000,,And 90 degree lines are also called perpendicular, because
Dialogue: 0,0:01:41.40,0:01:45.20,Default,,0000,0000,0000,,they are, I feel like saying because they are perpendicular,
Dialogue: 0,0:01:45.20,0:01:49.90,Default,,0000,0000,0000,,but because one is going completely vertical while the other is going horizontal.
Dialogue: 0,0:01:49.90,0:01:56.40,Default,,0000,0000,0000,,Wow, it's actually amazingly difficult to find the exact right wording.
Dialogue: 0,0:01:56.40,0:02:03.50,Default,,0000,0000,0000,,But I think you get the idea. By definition, perpendicular lines are 90 degrees apart from each other.
Dialogue: 0,0:02:03.50,0:02:07.70,Default,,0000,0000,0000,,And you've seen this all the time in things like squares or rectangles.
Dialogue: 0,0:02:07.70,0:02:18.80,Default,,0000,0000,0000,,A rectangle is made up of a bunch of perpendicular lines, or lines at 90 degree angles.
Dialogue: 0,0:02:18.80,0:02:23.70,Default,,0000,0000,0000,,The way you draw a 90 degree angle is you draw a little box like that.
Dialogue: 0,0:02:23.70,0:02:29.30,Default,,0000,0000,0000,,That's the same thing as doing this.
Dialogue: 0,0:02:29.30,0:02:49.70,Default,,0000,0000,0000,,And you could even get wider angles. If you go above 90 degrees... this could be, I don't know, 135 degrees
Dialogue: 0,0:02:49.70,0:02:59.10,Default,,0000,0000,0000,,If you ever want to really measure the angles you could use a protractor.
Dialogue: 0,0:02:59.10,0:03:10.40,Default,,0000,0000,0000,,Then if you had it so wide that the two lines are actually almost forming a line...
Dialogue: 0,0:03:10.40,0:03:21.60,Default,,0000,0000,0000,,that's 180 degrees. And then you could keep going.
Dialogue: 0,0:03:21.60,0:03:36.90,Default,,0000,0000,0000,,If this angle is 135 degrees...
Dialogue: 0,0:03:36.90,0:03:55.80,Default,,0000,0000,0000,,There are 360 degrees in a circle. So this magenta angle would be 360 - 135 degrees
Dialogue: 0,0:03:55.80,0:04:05.40,Default,,0000,0000,0000,,that's 225 degrees.
Dialogue: 0,0:04:05.40,0:04:12.10,Default,,0000,0000,0000,,So you know degrees in a circle are 360 degrees, this is important to know.
Dialogue: 0,0:04:12.10,0:04:17.40,Default,,0000,0000,0000,,It's also important to know that if you go halfway around a circle,
Dialogue: 0,0:04:17.40,0:04:20.40,Default,,0000,0000,0000,,that's 180 degrees.
Dialogue: 0,0:04:20.40,0:04:21.40,Default,,0000,0000,0000,,Like if you viewed the\Npivot point as like,
Dialogue: 0,0:04:21.40,0:04:22.10,Default,,0000,0000,0000,,let's say, right here.
Dialogue: 0,0:04:22.10,0:04:23.20,Default,,0000,0000,0000,,I mean it looks like just\None line and it really is.
Dialogue: 0,0:04:23.20,0:04:24.40,Default,,0000,0000,0000,,But that's 180 degrees.
Dialogue: 0,0:04:24.40,0:04:27.60,Default,,0000,0000,0000,,And then if you go quarter\Nway around the circle,
Dialogue: 0,0:04:27.60,0:04:31.80,Default,,0000,0000,0000,,that's 90 degrees.
Dialogue: 0,0:04:31.80,0:04:32.90,Default,,0000,0000,0000,,\NAll right?
Dialogue: 0,0:04:32.90,0:04:34.10,Default,,0000,0000,0000,,Hopefully you're getting\Na bit of an intuition
Dialogue: 0,0:04:34.10,0:04:35.60,Default,,0000,0000,0000,,for what an angle is.
Dialogue: 0,0:04:35.60,0:04:40.40,Default,,0000,0000,0000,,So now I will teach you\Na bunch of very useful
Dialogue: 0,0:04:40.40,0:04:44.50,Default,,0000,0000,0000,,rules for angles.
Dialogue: 0,0:04:44.50,0:04:50.30,Default,,0000,0000,0000,,\NClear this.
Dialogue: 0,0:04:50.30,0:04:50.80,Default,,0000,0000,0000,,\NSo let me redraw.
Dialogue: 0,0:04:50.80,0:04:54.30,Default,,0000,0000,0000,,So if I had a line like this.
Dialogue: 0,0:04:54.30,0:04:56.90,Default,,0000,0000,0000,,I like using the colors, just\Nso I think it keeps you from
Dialogue: 0,0:04:56.90,0:05:04.10,Default,,0000,0000,0000,,getting completely bored.
Dialogue: 0,0:05:04.10,0:05:06.48,Default,,0000,0000,0000,,And it might not be completely\Nintuitive what I'm doing, but
Dialogue: 0,0:05:06.48,0:05:11.40,Default,,0000,0000,0000,,let's add an angle like that.
Dialogue: 0,0:05:11.40,0:05:14.80,Default,,0000,0000,0000,,And so, let's just say-- you\Nknow, I'm not measuring these
Dialogue: 0,0:05:14.80,0:05:19.40,Default,,0000,0000,0000,,exactly-- let's say that\Nthis is 30 degrees.
Dialogue: 0,0:05:19.40,0:05:27.30,Default,,0000,0000,0000,,We know that if we go all the\Nway around the circle, we know
Dialogue: 0,0:05:27.30,0:05:29.80,Default,,0000,0000,0000,,that that's 360 degrees.
Dialogue: 0,0:05:29.80,0:05:30.60,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:05:30.60,0:05:33.30,Default,,0000,0000,0000,,And that's a very ugly\Nlooking around the circle
Dialogue: 0,0:05:33.30,0:05:36.10,Default,,0000,0000,0000,,angle that I drew.
Dialogue: 0,0:05:36.10,0:05:40.10,Default,,0000,0000,0000,,So then we also know\Nthat this angle right
Dialogue: 0,0:05:40.10,0:05:44.60,Default,,0000,0000,0000,,here is 330 degrees.
Dialogue: 0,0:05:44.60,0:05:45.30,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:05:45.30,0:05:48.80,Default,,0000,0000,0000,,Because this angle plus this\Nmagenta angle is going to
Dialogue: 0,0:05:48.80,0:05:50.30,Default,,0000,0000,0000,,equal the whole circle.
Dialogue: 0,0:05:50.30,0:05:53.30,Default,,0000,0000,0000,,So this is equal\Nto 330 degrees.
Dialogue: 0,0:05:53.30,0:05:56.40,Default,,0000,0000,0000,,So remember that.
Dialogue: 0,0:05:56.40,0:05:58.50,Default,,0000,0000,0000,,The angles in a circle--\Nor there are 360
Dialogue: 0,0:05:58.50,0:06:01.30,Default,,0000,0000,0000,,degrees in a circle.
Dialogue: 0,0:06:01.30,0:06:05.50,Default,,0000,0000,0000,,I don't know if you remember.
Dialogue: 0,0:06:05.50,0:06:06.20,Default,,0000,0000,0000,,You probably don't.
Dialogue: 0,0:06:06.20,0:06:07.40,Default,,0000,0000,0000,,This was probably\Nbefore you were born.
Dialogue: 0,0:06:07.40,0:06:08.90,Default,,0000,0000,0000,,But there used to be a game\Ncalled 720, and it was a
Dialogue: 0,0:06:08.90,0:06:10.90,Default,,0000,0000,0000,,skateboarding game--\Nit was a video game.
Dialogue: 0,0:06:10.90,0:06:14.10,Default,,0000,0000,0000,,And the 720 was essentially\Nyou were trying to jump
Dialogue: 0,0:06:14.10,0:06:16.50,Default,,0000,0000,0000,,your skateboard and\Nspin around twice.
Dialogue: 0,0:06:16.50,0:06:18.50,Default,,0000,0000,0000,,And that's 720 degrees.
Dialogue: 0,0:06:18.50,0:06:22.60,Default,,0000,0000,0000,,If you go around a circle\Ntwice that's 720 degrees.
Dialogue: 0,0:06:22.60,0:06:24.30,Default,,0000,0000,0000,,If you just jump and\Nspin around once, you
Dialogue: 0,0:06:24.30,0:06:26.70,Default,,0000,0000,0000,,went 360 degrees.
Dialogue: 0,0:06:26.70,0:06:29.70,Default,,0000,0000,0000,,So you've probably heard this\Nin just popular culture.
Dialogue: 0,0:06:29.70,0:06:31.20,Default,,0000,0000,0000,,But anyway.
Dialogue: 0,0:06:31.20,0:06:32.90,Default,,0000,0000,0000,,So 360 degrees in a circle.
Dialogue: 0,0:06:32.90,0:06:35.80,Default,,0000,0000,0000,,And you could imagine half\Na circle is 180 degrees.
Dialogue: 0,0:06:35.80,0:06:40.20,Default,,0000,0000,0000,,So the other important thing to\Nrealize is, like we said, if
Dialogue: 0,0:06:40.20,0:06:43.70,Default,,0000,0000,0000,,we go halfway around the\Ncircle it's 180 degrees.
Dialogue: 0,0:06:43.70,0:06:50.90,Default,,0000,0000,0000,,But if we have two angles that\Nadd up to that-- so let's say.
Dialogue: 0,0:06:50.90,0:06:53.70,Default,,0000,0000,0000,,I don't know if these lines are\Nthick enough for you to see.
Dialogue: 0,0:06:53.70,0:06:58.10,Default,,0000,0000,0000,,Let me draw something thicker.
Dialogue: 0,0:06:58.10,0:06:59.70,Default,,0000,0000,0000,,It doesn't look ideal,\Nbut you get the idea.
Dialogue: 0,0:06:59.70,0:07:11.60,Default,,0000,0000,0000,,So if we have this\Nangle, let's call it x.
Dialogue: 0,0:07:11.60,0:07:19.50,Default,,0000,0000,0000,,And then this angle is y.
Dialogue: 0,0:07:19.50,0:07:24.00,Default,,0000,0000,0000,,What do we know about the\Nrelationship between x and y?
Dialogue: 0,0:07:24.00,0:07:28.30,Default,,0000,0000,0000,,Well, we know that the entire\Nangle is half of a circle.
Dialogue: 0,0:07:28.30,0:07:28.80,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:07:28.80,0:07:31.70,Default,,0000,0000,0000,,So that's 180 degrees.
Dialogue: 0,0:07:31.70,0:07:34.50,Default,,0000,0000,0000,,That's 180 degrees,\Nthis entire angle.
Dialogue: 0,0:07:34.50,0:07:42.60,Default,,0000,0000,0000,,So what are angles x and\Ny going to add up to?
Dialogue: 0,0:07:42.60,0:07:44.90,Default,,0000,0000,0000,,I'm trying to stay\Ncolor consistent.
Dialogue: 0,0:07:44.90,0:07:51.10,Default,,0000,0000,0000,,x plus y are going to\Nequal-- I'm color blind,
Dialogue: 0,0:07:51.10,0:07:54.80,Default,,0000,0000,0000,,I think-- 180 degrees.
Dialogue: 0,0:07:54.80,0:08:00.40,Default,,0000,0000,0000,,Or you could write y is\Nequal to 180 minus x.
Dialogue: 0,0:08:00.40,0:08:05.00,Default,,0000,0000,0000,,Or x is equal to 180 minus y.
Dialogue: 0,0:08:05.00,0:08:09.10,Default,,0000,0000,0000,,But if x plus y are equal to\N180 degrees-- and you can see
Dialogue: 0,0:08:09.10,0:08:11.90,Default,,0000,0000,0000,,that it makes sense that they\Ndo-- if you add the two angles
Dialogue: 0,0:08:11.90,0:08:14.90,Default,,0000,0000,0000,,you go halfway around a circle.
Dialogue: 0,0:08:14.90,0:08:20.40,Default,,0000,0000,0000,,Then that tells us that x and y\Nare-- and this is a fancy word,
Dialogue: 0,0:08:20.40,0:08:22.90,Default,,0000,0000,0000,,and it's just good to commit\Nthis to memory-- they are
Dialogue: 0,0:08:22.90,0:08:36.30,Default,,0000,0000,0000,,supplementary angles.
Dialogue: 0,0:08:36.30,0:08:39.80,Default,,0000,0000,0000,,That's when you add\Nto 180 degrees.
Dialogue: 0,0:08:39.80,0:08:45.70,Default,,0000,0000,0000,,Now what if we had\Nthis situation.
Dialogue: 0,0:08:45.70,0:08:48.60,Default,,0000,0000,0000,,Oh my God, that was horrible.
Dialogue: 0,0:08:48.60,0:08:53.10,Default,,0000,0000,0000,,Undo.
Dialogue: 0,0:08:53.10,0:08:57.00,Default,,0000,0000,0000,,Let's say I had this situation.
Dialogue: 0,0:08:57.00,0:08:57.80,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:08:57.80,0:09:00.30,Default,,0000,0000,0000,,I draw two perpendicular lines.
Dialogue: 0,0:09:00.30,0:09:00.90,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:09:00.90,0:09:03.20,Default,,0000,0000,0000,,So this is going a quarter\Nway around the circle.
Dialogue: 0,0:09:03.20,0:09:03.70,Default,,0000,0000,0000,,All right.
Dialogue: 0,0:09:03.70,0:09:09.40,Default,,0000,0000,0000,,Let's say this entire angle\Nhere-- I'm drawing it really
Dialogue: 0,0:09:09.40,0:09:10.60,Default,,0000,0000,0000,,big-- that's 90 degrees.
Dialogue: 0,0:09:10.60,0:09:11.10,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:09:11.10,0:09:12.30,Default,,0000,0000,0000,,They're perpendicular.
Dialogue: 0,0:09:12.30,0:09:19.70,Default,,0000,0000,0000,,And now if I had two\Nangles within that.
Dialogue: 0,0:09:19.70,0:09:21.60,Default,,0000,0000,0000,,So now if I have two angles\Nhere-- so let's say that this
Dialogue: 0,0:09:21.60,0:09:27.20,Default,,0000,0000,0000,,is x and this is y-- what\Ndo x and y add up to?
Dialogue: 0,0:09:27.20,0:09:32.20,Default,,0000,0000,0000,,Well, x plus y is 90.
Dialogue: 0,0:09:32.20,0:09:38.90,Default,,0000,0000,0000,,And we can say that x and\Ny are complementary.
Dialogue: 0,0:09:38.90,0:09:43.00,Default,,0000,0000,0000,,And it's important to not get\Nconfused between the two.
Dialogue: 0,0:09:43.00,0:09:48.20,Default,,0000,0000,0000,,Just remember complementary\Nmeans two angles add up to 90
Dialogue: 0,0:09:48.20,0:09:50.50,Default,,0000,0000,0000,,degrees, supplementary means\Nthat two angles add
Dialogue: 0,0:09:50.50,9:59:59.99,Default,,0000,0000,0000,,up to 180 degrees.