-
So let's review everything that
we know so far, because it's
-
good to keep reviewing.
-
Because these are things
you should never forget
-
the rest of your life.
-
So if I have a line and if I
draw an angle that goes--
-
let's say this is the
pivot point, right?
-
If I go all the way around
the line, or in a circle,
-
that's 360 degrees.
-
11
00:00:23,97 --> 00:00:27,43
We learned that there are
360 degrees in a circle.
-
Right?
-
We also learned that if
I have lines like this.
-
If I have two angles-- let
me draw it like that.
-
16
00:00:43,71 --> 00:00:49,49
And this is angle x.
-
This is angle y.
-
19
00:00:54,122 --> 00:00:57,825
x and y are supplementary.
-
21
00:01:04,24 --> 00:01:07,63
And that just means that
they add up to 180 degrees.
-
x plus y is equal
to 180 degrees.
-
And why does that make sense?
-
Because look, if we add
up x plus y we have gone
-
halfway around the circle.
-
So that's 180 degrees, right?
-
So hopefully we
have learned that.
-
And then let me switch colors
for the sake of variety.
-
Let me use my line tool.
-
If I have-- let's see,
I'm going to draw
-
perpendicular lines.
-
If I have that line, and
then I have that line.
-
And they are perpendicular.
-
And then I have another line.
-
Let's say it goes like that.
-
39
00:01:59,83 --> 00:02:03,73
And then I say that
this is angle x.
-
Woops.
-
This is angle x.
-
And this is angle y.
-
44
00:02:12,29 --> 00:02:16,04
Well, I said this line and this
line are perpendicular, right?
-
So that means that they
intersect at a 90 degree angle.
-
So we know that this whole
thing is 90 degrees.
-
48
00:02:24,07 --> 00:02:26,01
And so what do we
know about x plus y?
-
Well, x plus y is going
to equal 90 degrees.
-
51
00:02:34,13 --> 00:02:41,33
Or we could say that x
and y are complementary.
-
And I always get confused
between supplementary
-
and complementary.
-
You just got to memorize it.
-
I don't know if there's
any-- let's see, is
-
there any easy way?
-
180, supplementary.
-
You could say that 180-- 100
starts with an O, which
-
supplementary does
not start with.
-
So there.
-
There's your mnemonic.
-
Complementary.
-
And 90 starts with an N,
and complementary does
-
not start with an N.
-
That's your other mnemonic.
-
Complementary.
-
68
00:03:15,42 --> 00:03:16,59
I don't know if I'm
spelling it right.
-
Who cares?
-
Let's move on.
-
So let's learn some more
stuff about angles.
-
And what I'm going to do is I'm
going to give you an arsenal,
-
and then once you have that
arsenal you can just tackle
-
these beastly problems that
I'm going to throw at you.
-
So just take these for granted
right now, and then in a few
-
videos, probably, we're
going to tackle some
-
beastly problems.
-
79
00:03:38,22 --> 00:03:40,48
And you know, I'm
using variables here.
-
And if you're not familiar
with variables you
-
can put numbers here.
-
If x was 30 degrees, then y
is going to be 60 degrees.
-
Right?
-
Or in this case, if x is, I
don't know, 45 degrees, then y
-
is going to be 135 degrees.
-
That other way.
-
Let me draw another property of
angles of intersecting lines.
-
So if I have two angles, two
lines that intersect like this.
-
90
00:04:08,56 --> 00:04:10,76
So a couple of
interesting things.
-
So first, I'm going to teach
you about opposite angles.
-
93
00:04:17,49 --> 00:04:19,51
Let me switch colors.
-
Let me switch to yellow.
-
So if this is x degrees, then
it turns out that the angle
-
opposite to it is also
equal to x degrees.
-
98
00:04:40,43 --> 00:04:42,18
And you don't believe me?
-
Well let me prove it to you.
-
Let's say we call this,
I don't know, let's
-
call this y degrees.
-
Right?
-
And I'm going to prove
to you that the x and
-
the y are the same.
-
Well what do we know already?
-
Let's call this other angle--
and I'm doing this to
-
confuse you-- angle z.
-
Well what do we know about
angle x and angle z?
-
It may not be obvious to you
because I've drawn it slightly
-
different, but I'll give you
a small hint with
-
an appropriately
interesting color.
-
So what angle is this
whole thing right here?
-
Well I'm just going
along a line, right?
-
That's halfway around a circle.
-
So what does x plus z equal?
-
Well, x plus z is going to
equal that larger angle.
-
x plus purple z is going to
equal-- I think I'll switch to
-
the blue; maybe it's taking too
much time for me to switch--
-
is equal to 180 degrees.
-
Or x and z are supplementary.
-
124
00:06:09,24 --> 00:06:10,63
I've run out of space.
-
So what do we know about z?
-
Well z is equal to 180 minus x.
-
Right?
-
Because x plus z is 180.
-
Fine.
-
Now, what's the relationship
between z and y?
-
Well, z and y are
also supplementary.
-
Because look, if I
drew this angle here.
-
Look at this big angle.
-
135
00:06:42,07 --> 00:06:42,69
What angle is that?
-
Well once again I'm still going
halfway around the circle.
-
Right?
-
But now I'm using this
line right here.
-
So that's 180 degrees.
-
So we know that angle z
plus angle y is also
-
equal to 180 degrees.
-
143
00:07:05,54 --> 00:07:06,82
Right?
-
Or, I don't want to keep
writing it, but z and y
-
are also supplementary.
-
But we just figured out
that z is 180 minus x.
-
Right?
-
So let's just substitute
that back in here.
-
So we get 180 minus x plus
y is equal to 180 degrees.
-
Why don't we subtract 180
degrees from both sides
-
of this equation.
-
That cancels out, and we get
minus x plus y is equal to 0.
-
And then add x to both sides
of this equation, and
-
we get y is equal to x.
-
So x is equal to y.
-
And if you've played around
with this, if you just drew a
-
bunch of straight lines and
they intersected at different
-
angles, I think when you
eyeball it it would make sense.
-
And then similarly, if that's z
then the other opposite angle
-
here is also z degrees.
-
So what do we know now?
-
The total angles in a
circle, 360 degrees.
-
When two angles kind of
combine, go halfway around the
-
circle-- or they combine,
kind of form a line.
-
There's different ways
you can think about it.
-
We know they're supplementary.
-
They add up to 180 degrees.
-
x plus y is 180 degrees.
-
If they add up to 90
it's complementary.
-
x plus y is 90.
-
And then opposite angles
are equal to each other.
-
Right?
-
This angle is equal
to this angle.
-
And then this angle is going to
be equal to this angle for the
-
same reason-- because
it's opposite.
-
In the next video I'm going
to show you about parallel
-
lines and transversals.
-
More fancy words for what
I think are fairly
-
straightforward concepts.
-
I'll see you in the next video.
