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Hello. In this series of presentations, I'm gonna try

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to teach you everything you need to know about triangles and angles and parallel lines

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and this is probably the highest-yield information that you could ever learn, especially in terms of the standardized tests.

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And then when we've learned all the rules we'll play something I call the Angle Game,

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which is essentially what the SAT makes you do over and over again.

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So let's start with some basics.You know what an angles is.

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Well actually maybe you don't know what an angle is.

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If I have two lines...

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and they intersect at some point,

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the angle is a measure of exactly how wide the intersection is between those two lines.

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So this is the angle. An angle is how wide those two lines open up.

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And they're measured either in degrees or radiants. And for the sake of most geometry classes we'll use degrees.

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When we start doing Trigonometry we'll use radiants.

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And you're probably familiar with this. Zero degrees would be two lines on top of each other...

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this if I were to just eyeball it looks like 45 degrees.

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If I had the lines even wider apart, like that, that's 90 degrees.

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And 90 degree lines are also called perpendicular, because

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they are, I feel like saying because they are perpendicular,

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but because one is going completely vertical while the other is going horizontal.

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Wow, it's actually amazingly difficult to find the exact right wording.

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But I think you get the idea. By definition, perpendicular lines are 90 degrees apart from each other.

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And you've seen this all the time in things like squares or rectangles.

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A rectangle is made up of a bunch of perpendicular lines, or lines at 90 degree angles.

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The way you draw a 90 degree angle is you draw a little box like that.

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That's the same thing as doing this.

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And you could even get wider angles. If you go above 90 degrees... this could be, I don't know, 135 degrees

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If you ever want to really measure the angles you could use a protractor.

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Then if you had it so wide that the two lines are actually almost forming a line...

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that's 180 degrees. And then you could keep going.

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If this angle is 135 degrees...

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There are 360 degrees in a circle. So this magenta angle would be 360 - 135 degrees

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that's 225 degrees.

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So you know degrees in a circle are 360 degrees, this is important to know.

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It's also important to know that if you go halfway around a circle,

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that's 180 degrees.

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Like if you viewed the[br]pivot point as like,

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let's say, right here.

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I mean it looks like just[br]one line and it really is.

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But that's 180 degrees.

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And then if you go quarter[br]way around the circle,

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that's 90 degrees.

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[br]All right?

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Hopefully you're getting[br]a bit of an intuition

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for what an angle is.

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So now I will teach you[br]a bunch of very useful

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rules for angles.

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[br]Clear this.

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[br]So let me redraw.

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So if I had a line like this.

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I like using the colors, just[br]so I think it keeps you from

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getting completely bored.

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And it might not be completely[br]intuitive what I'm doing, but

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let's add an angle like that.

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And so, let's just say-- you[br]know, I'm not measuring these

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exactly-- let's say that[br]this is 30 degrees.

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We know that if we go all the[br]way around the circle, we know

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that that's 360 degrees.

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Right?

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And that's a very ugly[br]looking around the circle

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angle that I drew.

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So then we also know[br]that this angle right

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here is 330 degrees.

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Right?

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Because this angle plus this[br]magenta angle is going to

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equal the whole circle.

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So this is equal[br]to 330 degrees.

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So remember that.

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The angles in a circle--[br]or there are 360

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degrees in a circle.

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I don't know if you remember.

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You probably don't.

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This was probably[br]before you were born.

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But there used to be a game[br]called 720, and it was a

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skateboarding game--[br]it was a video game.

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And the 720 was essentially[br]you were trying to jump

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your skateboard and[br]spin around twice.

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And that's 720 degrees.

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If you go around a circle[br]twice that's 720 degrees.

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If you just jump and[br]spin around once, you

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went 360 degrees.

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So you've probably heard this[br]in just popular culture.

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But anyway.

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So 360 degrees in a circle.

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And you could imagine half[br]a circle is 180 degrees.

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So the other important thing to[br]realize is, like we said, if

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we go halfway around the[br]circle it's 180 degrees.

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But if we have two angles that[br]add up to that-- so let's say.

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I don't know if these lines are[br]thick enough for you to see.

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Let me draw something thicker.

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It doesn't look ideal,[br]but you get the idea.

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So if we have this[br]angle, let's call it x.

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And then this angle is y.

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What do we know about the[br]relationship between x and y?

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Well, we know that the entire[br]angle is half of a circle.

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Right?

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So that's 180 degrees.

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That's 180 degrees,[br]this entire angle.

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So what are angles x and[br]y going to add up to?

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I'm trying to stay[br]color consistent.

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x plus y are going to[br]equal-- I'm color blind,

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I think-- 180 degrees.

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Or you could write y is[br]equal to 180 minus x.

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Or x is equal to 180 minus y.

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But if x plus y are equal to[br]180 degrees-- and you can see

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that it makes sense that they[br]do-- if you add the two angles

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you go halfway around a circle.

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Then that tells us that x and y[br]are-- and this is a fancy word,

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and it's just good to commit[br]this to memory-- they are

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supplementary angles.

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That's when you add[br]to 180 degrees.

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Now what if we had[br]this situation.

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Oh my God, that was horrible.

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Undo.

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Let's say I had this situation.

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Let's see.

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I draw two perpendicular lines.

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Right?

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So this is going a quarter[br]way around the circle.

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All right.

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Let's say this entire angle[br]here-- I'm drawing it really

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big-- that's 90 degrees.

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Right?

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They're perpendicular.

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And now if I had two[br]angles within that.

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So now if I have two angles[br]here-- so let's say that this

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is x and this is y-- what[br]do x and y add up to?

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Well, x plus y is 90.

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And we can say that x and[br]y are complementary.

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And it's important to not get[br]confused between the two.

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Just remember complementary[br]means two angles add up to 90

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degrees, supplementary means[br]that two angles add

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up to 180 degrees.