[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.63,0:00:10.00,Default,,0000,0000,0000,,Let's say I have an angle ABC, and it looks somethings like this, so its vertex is going to be at 'B',
Dialogue: 0,0:00:10.00,0:00:15.60,Default,,0000,0000,0000,,Maybe 'A' sits right over here, and 'C' sits right over there.
Dialogue: 0,0:00:15.60,0:00:23.80,Default,,0000,0000,0000,,And then also let's say we have another angle called DAB, actually let me call it DBA,
Dialogue: 0,0:00:23.80,0:00:26.33,Default,,0000,0000,0000,,I want to have the vertex once again at 'B'.
Dialogue: 0,0:00:26.33,0:00:34.00,Default,,0000,0000,0000,,So let's say it looks like this, so this right over here is our point 'D'.
Dialogue: 0,0:00:34.00,0:00:41.73,Default,,0000,0000,0000,,And let's say we know the measure of angle DBA, let's say we know that that's equal to 40 degrees.
Dialogue: 0,0:00:41.73,0:00:45.87,Default,,0000,0000,0000,,So this angle right over here, its measure is equal to 40 degrees,
Dialogue: 0,0:00:45.87,0:00:56.60,Default,,0000,0000,0000,,And let's say we know that the measure of angle ABC is equal to 50 degrees.
Dialogue: 0,0:00:56.60,0:00:58.73,Default,,0000,0000,0000,,Right, so there's a bunch of interesting things happening over here,
Dialogue: 0,0:00:58.73,0:01:02.67,Default,,0000,0000,0000,,the first interesting thing that you might realize is that both of these angles
Dialogue: 0,0:01:02.67,0:01:06.13,Default,,0000,0000,0000,,share a side, if you view these as rays, they could be lines,
Dialogue: 0,0:01:06.13,0:01:08.40,Default,,0000,0000,0000,,line segments or rays, but if you view them as rays,
Dialogue: 0,0:01:08.40,0:01:13.27,Default,,0000,0000,0000,,then they both share the ray BA, and when you have two angles
Dialogue: 0,0:01:13.27,0:01:16.93,Default,,0000,0000,0000,,like this that share the same side, these are called adjacent angles
Dialogue: 0,0:01:16.93,0:01:20.67,Default,,0000,0000,0000,,because the word adjacent literally means 'next to'.
Dialogue: 0,0:01:20.67,0:01:26.93,Default,,0000,0000,0000,,Adjacent, these are adjacent angles.
Dialogue: 0,0:01:26.93,0:01:29.93,Default,,0000,0000,0000,,Now there's something else you might notice that's interesting here,
Dialogue: 0,0:01:29.93,0:01:33.07,Default,,0000,0000,0000,,we know that the measure of angle DBA is 40 degreees
Dialogue: 0,0:01:33.07,0:01:35.93,Default,,0000,0000,0000,,and the measure of angle ABC is 50 degrees
Dialogue: 0,0:01:35.93,0:01:42.13,Default,,0000,0000,0000,,and you might be able to guess what the measure of angle DBC is,
Dialogue: 0,0:01:42.13,0:01:47.07,Default,,0000,0000,0000,,the measure of angle DBC, if we drew a protractor over here
Dialogue: 0,0:01:47.07,0:01:49.80,Default,,0000,0000,0000,,I'm not going to draw it, it will make my drawing all messy,
Dialogue: 0,0:01:49.80,0:01:51.87,Default,,0000,0000,0000,,but if we, well I'll draw it really fast,
Dialogue: 0,0:01:51.87,0:01:55.80,Default,,0000,0000,0000,,So, if we had a protractor over here, clearly this is opening up to 50 degrees,
Dialogue: 0,0:01:55.80,0:01:59.13,Default,,0000,0000,0000,,and this is going another 40 degrees, so if you wanted to say
Dialogue: 0,0:01:59.13,0:02:01.47,Default,,0000,0000,0000,,what the measure of angle DBC is,
Dialogue: 0,0:02:01.47,0:02:05.80,Default,,0000,0000,0000,,it would be, it would essentially be the the sum of 40 degrees and 50 degrees.
Dialogue: 0,0:02:05.80,0:02:08.47,Default,,0000,0000,0000,,And let me delete all this stuff right here, to keep things clean,
Dialogue: 0,0:02:08.47,0:02:13.93,Default,,0000,0000,0000,,So the measure of angle DBC would be equal to 90 degrees
Dialogue: 0,0:02:13.93,0:02:16.60,Default,,0000,0000,0000,,and we already know that 90 degrees is a special angle,
Dialogue: 0,0:02:16.60,0:02:22.67,Default,,0000,0000,0000,,this is a right angle, this is a right angle.
Dialogue: 0,0:02:22.67,0:02:30.00,Default,,0000,0000,0000,,There's also a word for two angles whose sum add to 90 degrees,
Dialogue: 0,0:02:30.00,0:02:31.60,Default,,0000,0000,0000,,and that is complementary.
Dialogue: 0,0:02:31.60,0:02:43.73,Default,,0000,0000,0000,,So we can also say that angle DBA and angles ABC are complementary.
Dialogue: 0,0:02:43.73,0:02:51.07,Default,,0000,0000,0000,,And that is because their measures add up to 90 degrees,
Dialogue: 0,0:02:51.07,0:02:57.33,Default,,0000,0000,0000,,So the measure of angle DBA plus the measure of angle ABC,
Dialogue: 0,0:02:57.33,0:03:03.87,Default,,0000,0000,0000,,is equal to 90 degrees, they form a right angle when you add them up.
Dialogue: 0,0:03:03.87,0:03:08.00,Default,,0000,0000,0000,,And just as another point of terminology, that's kind of related to right angles,
Dialogue: 0,0:03:08.00,0:03:14.40,Default,,0000,0000,0000,,when you form, when a right angle is formed, the two rays that form the right angle,
Dialogue: 0,0:03:14.40,0:03:17.60,Default,,0000,0000,0000,,or the two lines that form that right angle, or the two line segments,
Dialogue: 0,0:03:17.60,0:03:20.20,Default,,0000,0000,0000,,are called perpendicular.
Dialogue: 0,0:03:20.20,0:03:23.20,Default,,0000,0000,0000,,So because we know the measure of angle DBC is 90 degrees,
Dialogue: 0,0:03:23.91,0:03:27.36,Default,,0000,0000,0000,,or that angle DBC is a right angle, this tells us
Dialogue: 0,0:03:31.36,0:03:36.17,Default,,0000,0000,0000,,that DB, if I call them, maybe the line segment DB is
Dialogue: 0,0:03:36.67,0:03:47.40,Default,,0000,0000,0000,,perpendicular, is perpendicular to line segment BC,
Dialogue: 0,0:03:47.40,0:03:55.40,Default,,0000,0000,0000,,or we could even say that ray BD, is instead of using the word perpendicular
Dialogue: 0,0:03:55.40,0:03:59.53,Default,,0000,0000,0000,,there is sometimes this symbol right here, which just shows two perpendicular lines,
Dialogue: 0,0:03:59.53,0:04:03.53,Default,,0000,0000,0000,,DB is perpendicular to BC
Dialogue: 0,0:04:03.53,0:04:07.00,Default,,0000,0000,0000,,So all of these are true statements here,
Dialogue: 0,0:04:07.00,0:04:11.80,Default,,0000,0000,0000,,and these come out of the fact that the angle formed between DB and BC
Dialogue: 0,0:04:11.80,0:04:14.93,Default,,0000,0000,0000,,that is a 90 degree angle.
Dialogue: 0,0:04:14.93,0:04:19.67,Default,,0000,0000,0000,,Now we have other words when our two angles add up to other things,
Dialogue: 0,0:04:19.67,0:04:24.60,Default,,0000,0000,0000,,so let's say for example I have one angle over here,
Dialogue: 0,0:04:24.60,0:04:31.13,Default,,0000,0000,0000,,that is, I'll just make up, let's just call this angle,
Dialogue: 0,0:04:31.13,0:04:38.27,Default,,0000,0000,0000,,let me just put some letters here to specify, 'X', 'Y' and 'Z'.
Dialogue: 0,0:04:38.27,0:04:45.80,Default,,0000,0000,0000,,Let's say that the measure of angle XYZ is equal to 60 degrees,
Dialogue: 0,0:04:45.80,0:04:53.67,Default,,0000,0000,0000,,and let's say you have another angle, that looks like this,
Dialogue: 0,0:04:53.67,0:05:01.93,Default,,0000,0000,0000,,and I'll call this, maybe 'M', 'N', 'O',
Dialogue: 0,0:05:01.93,0:05:08.13,Default,,0000,0000,0000,,and let's say that the measure of angle MNO is 120 degrees.
Dialogue: 0,0:05:08.13,0:05:12.33,Default,,0000,0000,0000,,So if you were to add the two measures of these, so let me write this down,
Dialogue: 0,0:05:12.33,0:05:24.67,Default,,0000,0000,0000,,the measure of angle MNO plus the measure of angle XYZ,
Dialogue: 0,0:05:24.67,0:05:30.93,Default,,0000,0000,0000,,is equal to, this is going to be equal to 120 degrees plus 60 degrees.
Dialogue: 0,0:05:30.93,0:05:35.80,Default,,0000,0000,0000,,Which is equal to 180 degrees, so if you add these two things up,
Dialogue: 0,0:05:35.80,0:05:39.20,Default,,0000,0000,0000,,you're essentially able to go halfway around the circle.
Dialogue: 0,0:05:39.20,0:05:44.33,Default,,0000,0000,0000,,Or throughout the entire half circle, or a semi-circle for a protractor.
Dialogue: 0,0:05:44.33,0:05:50.07,Default,,0000,0000,0000,,And when you have two angles that add up to 180 degrees, we call them supplementary angles
Dialogue: 0,0:05:50.07,0:05:53.67,Default,,0000,0000,0000,,I know it's a little hard to remember sometimes, 90 degrees is complementary,
Dialogue: 0,0:05:53.67,0:05:55.40,Default,,0000,0000,0000,,there are two angles complementing each other,
Dialogue: 0,0:05:55.40,0:06:04.33,Default,,0000,0000,0000,,and then if you add up to 180 degrees, you have supplementary angles,
Dialogue: 0,0:06:04.33,0:06:07.27,Default,,0000,0000,0000,,and if you have two supplementary angles that are adjacent,
Dialogue: 0,0:06:07.27,0:06:12.20,Default,,0000,0000,0000,,so they share a common side, so let me draw that over here,
Dialogue: 0,0:06:12.20,0:06:14.93,Default,,0000,0000,0000,,So let's say you have one angle that looks like this,
Dialogue: 0,0:06:14.93,0:06:19.13,Default,,0000,0000,0000,,And that you have another angle, so so let me put some letters here again,
Dialogue: 0,0:06:19.13,0:06:20.67,Default,,0000,0000,0000,,and I'll start re-using letters,
Dialogue: 0,0:06:20.67,0:06:28.33,Default,,0000,0000,0000,,so this is 'A', 'B', 'C', and you have another angle that looks like this,
Dialogue: 0,0:06:28.33,0:06:36.00,Default,,0000,0000,0000,,that looks like this, I already used 'C', that looks like this
Dialogue: 0,0:06:36.00,0:06:40.67,Default,,0000,0000,0000,,notice and let's say once again that this is 50 degrees,
Dialogue: 0,0:06:40.67,0:06:43.73,Default,,0000,0000,0000,,and this right over here is 130 degrees,
Dialogue: 0,0:06:43.73,0:06:49.60,Default,,0000,0000,0000,,clearly angle DBA plus angle ABC, if you add them together,
Dialogue: 0,0:06:49.60,0:06:53.33,Default,,0000,0000,0000,,you get 180 degrees.
Dialogue: 0,0:06:53.33,0:06:56.13,Default,,0000,0000,0000,,So they are supplementary, let me write that down,
Dialogue: 0,0:06:56.13,0:07:05.33,Default,,0000,0000,0000,,Angle DBA and angle ABC are supplementary,
Dialogue: 0,0:07:05.33,0:07:09.22,Default,,0000,0000,0000,,they add up to 180 degrees, but they are also adjacent angles,
Dialogue: 0,0:07:09.58,0:07:17.18,Default,,0000,0000,0000,,they are also adjacent, and because they are supplementary and they're adjacent,
Dialogue: 0,0:07:17.89,0:07:22.38,Default,,0000,0000,0000,,if you look at the broader angle, the angle formed from the sides they don't have in common,
Dialogue: 0,0:07:22.45,0:07:31.87,Default,,0000,0000,0000,,if you look at angle DBC, this is going to be essentially a straight line,
Dialogue: 0,0:07:31.87,0:07:36.73,Default,,0000,0000,0000,,which we can call a straight angle.
Dialogue: 0,0:07:36.73,0:07:40.73,Default,,0000,0000,0000,,So I've introduced you to a bunch of words here and now I think
Dialogue: 0,0:07:40.73,0:07:45.80,Default,,0000,0000,0000,,we have all of the tools we need to start doing some interesting proofs,
Dialogue: 0,0:07:45.80,0:07:50.87,Default,,0000,0000,0000,,and just to review here we talked about adjacent angles, and I guess any angles
Dialogue: 0,0:07:50.87,0:07:55.87,Default,,0000,0000,0000,,that add up to 90 degrees are considered to be complementary,
Dialogue: 0,0:07:55.87,0:07:57.53,Default,,0000,0000,0000,,this is adding up to 90 degrees.
Dialogue: 0,0:07:57.53,0:08:03.27,Default,,0000,0000,0000,,If they happen to be adjacent then the two outside sides will form a right angle,
Dialogue: 0,0:08:03.27,0:08:08.13,Default,,0000,0000,0000,,when you have a right angle the two sides of a right angle are considered to be
Dialogue: 0,0:08:08.13,0:08:10.13,Default,,0000,0000,0000,,perpendicular.
Dialogue: 0,0:08:10.13,0:08:13.40,Default,,0000,0000,0000,,And then if you have two angles that add up 180 degrees,
Dialogue: 0,0:08:13.40,0:08:17.27,Default,,0000,0000,0000,,they are considered supplementary, and then if they happen to be adjacent,
Dialogue: 0,0:08:17.27,0:08:19.86,Default,,0000,0000,0000,,they will form a straight angle.
Dialogue: 0,0:08:20.02,0:08:22.94,Default,,0000,0000,0000,,Or another way of saying itis that if you have a straight angle,
Dialogue: 0,0:08:24.67,0:08:26.27,Default,,0000,0000,0000,,and you have one of the angles, the other angle
Dialogue: 0,0:08:26.27,0:08:29.27,Default,,0000,0000,0000,,is going to be supplementary to it, they're going to add up to 180 degrees.
Dialogue: 0,0:08:29.27,9:59:59.99,Default,,0000,0000,0000,,So I'll leave you there.