Hello.
In this series of presentations I'm going to try to teach you
everything you need to know about triangles and angles
and parallel lines.
And this is probably the highest yield information that
you could ever learn, and especially in terms of
standardized tests.
And then when we've learned all the rules we'll play something
that I call the angle game, which is essentially what the
SAT makes you do over and over again.
So let's start with some basics.
Well, you know what an angle is.
Well actually, maybe you don't know what an angle is.
And I'll tell you what an angle is.
If I have two lines-- I'm going to draw a thicker
line than that.
If I have two lines and they intersect at some point, the
angle is a measure of exactly kind of how wide the
intersection is between those two lines.
Let me use a better tool.
So this is the angle.
An angle is how wide those two lines kind of open up.
And they're measured either in degrees or radians, and for the
sake of most of a geometry class we'll use degrees.
And when we start doing trigonometry you'll
learn radians.
Or maybe you could learn it now.
And you're probably familiar with this.
0 degrees would be these two lines on top of each other.
This, if I were to just eyeball it, looks like 45 degrees.
If I had the lines even wider apart like that,
that's 90 degrees.
And 90 degree lines are also called perpendicular, because
they are-- I feel like saying, because they are
perpendicular-- but because one is going completely vertical
while the other is going horizontal.
It's actually amazingly difficult to find the
exact right wording.
But I think you get the idea.
By definition, perpendicular lines have a 90 degree
apart from each other.
And, you know, you've seen this all the time in things like
squares and rectangles.
If I were to draw a rectangle like that.
Right?
A rectangle is made up of a bunch of perpendicular lines,
or lines at 90 degree angles.
So example.
These two lines are at a 90 degree angle.
The way you draw a 90 degree angle is you draw
a little box like that.
That's the same thing as doing this-- as doing
a 90 degree angle.
And you could even get wider angles.
So if you go above 90 degrees.
So let's say I had lines like this.
So this would be-- I don't know, I'm just eyeballing
it-- 135 degrees or something like that.
If you ever want to really measure the angles, you can use
something called a protractor.
That's a tool maybe your teachers can help you use that.
So that'd be 135 degrees.
And then if you had it so wide that the two lines are actually
almost forming a line, then this becomes 180 degrees.
It's almost like one line.
Right?
This is 180 degrees.
And then you can keep going.
So if this angle here is 135 degrees, you can actually also
measure this angle right here.
Let me do it in a different color just to add some variety.
So then this angle right here.
So the angles in a circle are there are 360
degrees in a circle.
So if this is 135, this magenta angle would be 360 degrees
minus 135 degrees.
And that's equal to what?
That's 225 degrees, is this magenta angle.
And then we could do other things like that.
So one, you know that the degrees in the circle
are 360 degrees.
This is important to know.
Degrees in a circle are 360 degrees.
It's also important to know that if you just go kind of
halfway around a circle, like we did here,
that's 180 degrees.
Like if you viewed the pivot point as like,
let's say, right here.
I mean it looks like just one line and it really is.
But that's 180 degrees.
And then if you go quarter way around the circle,
that's 90 degrees.
All right?
Hopefully you're getting a bit of an intuition
for what an angle is.
So now I will teach you a bunch of very useful
rules for angles.
Clear this.
So let me redraw.
So if I had a line like this.
I like using the colors, just so I think it keeps you from
getting completely bored.
And it might not be completely intuitive what I'm doing, but
let's add an angle like that.
And so, let's just say-- you know, I'm not measuring these
exactly-- let's say that this is 30 degrees.
We know that if we go all the way around the circle, we know
that that's 360 degrees.
Right?
And that's a very ugly looking around the circle
angle that I drew.
So then we also know that this angle right
here is 330 degrees.
Right?
Because this angle plus this magenta angle is going to
equal the whole circle.
So this is equal to 330 degrees.
So remember that.
The angles in a circle-- or there are 360
degrees in a circle.
I don't know if you remember.
You probably don't.
This was probably before you were born.
But there used to be a game called 720, and it was a
skateboarding game-- it was a video game.
And the 720 was essentially you were trying to jump
your skateboard and spin around twice.
And that's 720 degrees.
If you go around a circle twice that's 720 degrees.
If you just jump and spin around once, you
went 360 degrees.
So you've probably heard this in just popular culture.
But anyway.
So 360 degrees in a circle.
And you could imagine half a circle is 180 degrees.
So the other important thing to realize is, like we said, if
we go halfway around the circle it's 180 degrees.
But if we have two angles that add up to that-- so let's say.
I don't know if these lines are thick enough for you to see.
Let me draw something thicker.
It doesn't look ideal, but you get the idea.
So if we have this angle, let's call it x.
And then this angle is y.
What do we know about the relationship between x and y?
Well, we know that the entire angle is half of a circle.
Right?
So that's 180 degrees.
That's 180 degrees, this entire angle.
So what are angles x and y going to add up to?
I'm trying to stay color consistent.
x plus y are going to equal-- I'm color blind,
I think-- 180 degrees.
Or you could write y is equal to 180 minus x.
Or x is equal to 180 minus y.
But if x plus y are equal to 180 degrees-- and you can see
that it makes sense that they do-- if you add the two angles
you go halfway around a circle.
Then that tells us that x and y are-- and this is a fancy word,
and it's just good to commit this to memory-- they are
supplementary angles.
That's when you add to 180 degrees.
Now what if we had this situation.
Oh my God, that was horrible.
Undo.
Let's say I had this situation.
Let's see.
I draw two perpendicular lines.
Right?
So this is going a quarter way around the circle.
All right.
Let's say this entire angle here-- I'm drawing it really
big-- that's 90 degrees.
Right?
They're perpendicular.
And now if I had two angles within that.
So now if I have two angles here-- so let's say that this
is x and this is y-- what do x and y add up to?
Well, x plus y is 90.
And we can say that x and y are complementary.
And it's important to not get confused between the two.
Just remember complementary means two angles add up to 90
degrees, supplementary means that two angles add
up to 180 degrees.
I'm running out of time, so I will see you in the next video.