WEBVTT

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Let's say I have an angle ABC, and it looks somethings like this, so its vertex is going to be at 'B',

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Maybe 'A' sits right over here, and 'C' sits right over there.

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And then also let's say we have another angle called DAB, actually let me call it DBA,

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I want to have the vertex once again at 'B'.

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So let's say it looks like this, so this right over here is our point 'D'.

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And let's say we know the measure of angle DBA, let's say we know that that's equal to 40 degrees.

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So this angle right over here, its measure is equal to 40 degrees,

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And let's say we know that the measure of angle ABC is equal to 50 degrees.

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Right, so there's a bunch of interesting things happening over here,

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the first interesting thing that you might realize is that both of these angles

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share a side, if you view these as rays, they could be lines,

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line segments or rays, but if you view them as rays,

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then they both share the ray BA, and when you have two angles

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like this that share the same side, these are called adjacent angles

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because the word adjacent literally means 'next to'.

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Adjacent, these are adjacent angles.

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Now there's something else you might notice that's interesting here,

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we know that the measure of angle DBA is 40 degreees

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and the measure of angle ABC is 50 degrees

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and you might be able to guess what the measure of angle DBC is,

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the measure of angle DBC, if we drew a protractor over here

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I'm not going to draw it, it will make my drawing all messy,

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but if we, well I'll draw it really fast,

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So, if we had a protractor over here, clearly this is opening up to 50 degrees,

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and this is going another 40 degrees, so if you wanted to say

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what the measure of angle DBC is,

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it would be, it would essentially be the the sum of 40 degrees and 50 degrees.

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And let me delete all this stuff right here, to keep things clean,

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So the measure of angle DBC would be equal to 90 degrees

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and we already know that 90 degrees is a special angle,

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this is a right angle, this is a right angle.

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There's also a word for two angles whose sum add to 90 degrees,

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and that is complementary.

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So we can also say that angle DBA and angles ABC are complementary.

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And that is because their measures add up to 90 degrees,

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So the measure of angle DBA plus the measure of angle ABC,

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is equal to 90 degrees, they form a right angle when you add them up.

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And just as another point of terminology, that's kind of related to right angles,

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when you form, when a right angle is formed, the two rays that form the right angle,

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or the two lines that form that right angle, or the two line segments,

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are called perpendicular.

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So because we know the measure of angle DBC is 90 degrees,

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or that angle DBC is a right angle, this tells us

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that DB, if I call them, maybe the line segment DB is

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perpendicular, is perpendicular to line segment BC,

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or we could even say that ray BD, is instead of using the word perpendicular

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there is sometimes this symbol right here, which just shows two perpendicular lines,

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DB is perpendicular to BC

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So all of these are true statements here,

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and these come out of the fact that the angle formed between DB and BC

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that is a 90 degree angle.

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Now we have other words when our two angles add up to other things,

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so let's say for example I have one angle over here,

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that is, I'll just make up, let's just call this angle,

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let me just put some letters here to specify, 'X', 'Y' and 'Z'.

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Let's say that the measure of angle XYZ is equal to 60 degrees,

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and let's say you have another angle, that looks like this,

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and I'll call this, maybe 'M', 'N', 'O',

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and let's say that the measure of angle MNO is 120 degrees.

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So if you were to add the two measures of these, so let me write this down,

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the measure of angle MNO plus the measure of angle XYZ,

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is equal to, this is going to be equal to 120 degrees plus 60 degrees.

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Which is equal to 180 degrees, so if you add these two things up,

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you're essentially able to go halfway around the circle.

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Or throughout the entire half circle, or a semi-circle for a protractor.

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And when you have two angles that add up to 180 degrees, we call them supplementary angles

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I know it's a little hard to remember sometimes, 90 degrees is complementary,

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there are two angles complementing each other,

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and then if you add up to 180 degrees, you have supplementary angles,

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and if you have two supplementary angles that are adjacent,

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so they share a common side, so let me draw that over here,

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So let's say you have one angle that looks like this,

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And that you have another angle, so so let me put some letters here again,

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and I'll start re-using letters,

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so this is 'A', 'B', 'C', and you have another angle that looks like this,

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that looks like this, I already used 'C', that looks like this

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notice and let's say once again that this is 50 degrees,

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and this right over here is 130 degrees,

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clearly angle DBA plus angle ABC, if you add them together,

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you get 180 degrees.

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So they are supplementary, let me write that down,

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Angle DBA and angle ABC are supplementary,

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they add up to 180 degrees, but they are also adjacent angles,

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they are also adjacent, and because they are supplementary and they're adjacent,

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if you look at the broader angle, the angle formed from the sides they don't have in common,

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if you look at angle DBC, this is going to be essentially a straight line,

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which we can call a straight angle.

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So I've introduced you to a bunch of words here and now I think

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we have all of the tools we need to start doing some interesting proofs,

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and just to review here we talked about adjacent angles, and I guess any angles

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that add up to 90 degrees are considered to be complementary,

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this is adding up to 90 degrees.

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If they happen to be adjacent then the two outside sides will form a right angle,

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when you have a right angle the two sides of a right angle are considered to be

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perpendicular.

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And then if you have two angles that add up 180 degrees,

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they are considered supplementary, and then if they happen to be adjacent,

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they will form a straight angle.

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Or another way of saying itis that if you have a straight angle,

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and you have one of the angles, the other angle

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is going to be supplementary to it, they're going to add up to 180 degrees.

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So I'll leave you there.