WEBVTT

00:00:00.443 --> 00:00:02.206
- [Voiceover] What I wanna
talk about in this video

00:00:02.206 --> 00:00:05.260
is shapes with four sides,

00:00:05.260 --> 00:00:08.964
and the mathy word for
shapes with four sides

00:00:08.964 --> 00:00:10.798
is quadrilateral.

00:00:10.798 --> 00:00:12.062
Quadrilateral.

00:00:12.062 --> 00:00:14.559
And any time you see
quad as part of a word,

00:00:14.559 --> 00:00:17.426
it's a good, it's a good sign

00:00:17.426 --> 00:00:19.806
that you're dealing with
the number four somehow.

00:00:19.806 --> 00:00:22.859
So a quadrilateral is
something that has four sides.

00:00:22.859 --> 00:00:26.726
So that is a quadrilateral,

00:00:26.726 --> 00:00:29.755
this is a quadrilateral,

00:00:29.755 --> 00:00:32.159
this is a quadrilateral.

00:00:32.159 --> 00:00:33.378
They all have four sides.

00:00:33.378 --> 00:00:36.396
This is a quadrilateral.

00:00:36.396 --> 00:00:39.705
even this is a,

00:00:39.705 --> 00:00:42.456
let me make it look even weirder,

00:00:42.456 --> 00:00:45.579
even this is a quadrilateral.

00:00:45.579 --> 00:00:47.564
So what's not a quadrilateral?

00:00:47.564 --> 00:00:49.619
Well, a triangle would
not be a quadrilateral.

00:00:49.619 --> 00:00:50.524
It has three sides,

00:00:50.524 --> 00:00:51.638
one, two, three.

00:00:51.638 --> 00:00:53.635
So let's cross that out.

00:00:53.635 --> 00:00:55.714
A pentagon that has five sides,

00:00:55.714 --> 00:00:57.014
that would not be a quadrilateral.

00:00:57.014 --> 00:00:59.782
It has one, two, three, four, five sides.

00:00:59.782 --> 00:01:03.264
A circle that has, I guess
you could say, no sides,

00:01:03.264 --> 00:01:06.735
it's just one big curve, it's a circle.

00:01:06.735 --> 00:01:09.359
That's not going to be a quadrilateral.

00:01:09.359 --> 00:01:11.414
If you had six sides, seven
sides, a hundred sides,

00:01:11.414 --> 00:01:14.618
none of that is going
to be a quadrilateral.

00:01:14.618 --> 00:01:15.353
So now let's think about

00:01:15.353 --> 00:01:17.164
the different types of quadrilaterals,

00:01:17.164 --> 00:01:19.950
or the different categories
of quadrilaterals.

00:01:19.950 --> 00:01:23.085
So one is the parallelogram.

00:01:23.085 --> 00:01:26.766
So a parallelogram is a quadrilateral,

00:01:26.766 --> 00:01:28.066
and as we learn more math,

00:01:28.066 --> 00:01:31.211
we'll learn other ways
of thinking about this.

00:01:31.211 --> 00:01:35.367
It's a quadrilateral where
opposite sides are parallel.

00:01:35.367 --> 00:01:36.841
And parallel is just another way of saying

00:01:36.841 --> 00:01:39.268
that they're going in the same direction.

00:01:39.268 --> 00:01:41.061
So what do I mean by that?

00:01:41.061 --> 00:01:43.209
So something like this,

00:01:43.209 --> 00:01:45.229
something like this,

00:01:45.229 --> 00:01:47.423
would be a parallelogram.

00:01:47.423 --> 00:01:48.538
Why?

00:01:48.538 --> 00:01:52.315
Because this side is
opposite to this side,

00:01:52.315 --> 00:01:54.213
and they're pointed in the same direction.

00:01:54.213 --> 00:01:55.374
They're going,

00:01:55.374 --> 00:01:58.323
they're going, if I were to draw an arrow,

00:01:58.323 --> 00:01:59.623
if I were to draw an arrow here,

00:01:59.623 --> 00:02:04.139
those arrows are pointed in the same way.

00:02:04.139 --> 00:02:06.322
So those two sides are pointed,

00:02:06.322 --> 00:02:09.154
are parallel, is the word we say.

00:02:09.154 --> 00:02:11.941
And these two sides,

00:02:11.941 --> 00:02:15.296
these two sides right
over here are parallel.

00:02:15.296 --> 00:02:17.397
So this is a parallelogram.

00:02:17.397 --> 00:02:20.020
So what are other
examples of parallelogram?

00:02:20.020 --> 00:02:21.994
Well even your classic square,

00:02:21.994 --> 00:02:23.759
even your classic square,

00:02:23.759 --> 00:02:25.012
is a parallelogram.

00:02:25.012 --> 00:02:26.893
And we'll talk more about
what makes a square special.

00:02:26.893 --> 00:02:28.832
It's a special type of parallelogram

00:02:28.832 --> 00:02:31.595
because this side

00:02:31.595 --> 00:02:34.392
is going in the same
direction as that side,

00:02:34.392 --> 00:02:38.595
and this side, and this side,

00:02:38.595 --> 00:02:40.894
whoops, let me do that in yellow,

00:02:40.894 --> 00:02:44.794
and this side is parallel to that side.

00:02:44.794 --> 00:02:47.511
So what's not a parallelogram?

00:02:47.511 --> 00:02:49.833
Well, something like,

00:02:49.833 --> 00:02:53.065
something like this

00:02:53.065 --> 00:02:55.026
would not be a parallelogram.

00:02:55.026 --> 00:02:55.582
You might say, "Wait,

00:02:55.582 --> 00:02:57.882
"I see two opposite sides are parallel."

00:02:57.882 --> 00:03:02.224
You might say, "Look,
this is parallel to this."

00:03:02.224 --> 00:03:06.454
But then you would see that
this is not parallel to this.

00:03:06.454 --> 00:03:08.441
One way to think about some
things that are not parallel

00:03:08.441 --> 00:03:10.298
is if the lines kept going,

00:03:10.298 --> 00:03:12.677
they would cross each other at some point,

00:03:12.677 --> 00:03:14.279
while these lines,

00:03:14.279 --> 00:03:15.998
these lines right over here,

00:03:15.998 --> 00:03:18.180
they're never going to cross each other.

00:03:18.180 --> 00:03:19.933
So this one right over here

00:03:19.933 --> 00:03:21.720
is not a parallelogram.

00:03:21.720 --> 00:03:25.099
It has one set of opposite
sides being parallel,

00:03:25.099 --> 00:03:26.619
but not the other.

00:03:26.619 --> 00:03:29.616
Another example of something
that is not a parallelogram

00:03:29.616 --> 00:03:31.972
would be this one right over here,

00:03:31.972 --> 00:03:34.734
because none of the
opposite sides are parallel.

00:03:34.734 --> 00:03:38.299
So parallelogram, opposite
sides are parallel.

00:03:38.299 --> 00:03:39.948
So now let's talk about,

00:03:39.948 --> 00:03:44.050
let's talk about more
types of four sided shapes,

00:03:44.050 --> 00:03:46.256
or quadrilaterals.

00:03:46.256 --> 00:03:50.529
So the next one we'll
talk about is the rhombus.

00:03:50.529 --> 00:03:54.208
So the rhombus is a type of parallelogram.

00:03:54.208 --> 00:03:57.262
The opposite sides need to be parallel,

00:03:57.262 --> 00:04:00.999
but that's not, by itself,
that doesn't make it a rhombus.

00:04:00.999 --> 00:04:03.020
The opposite sides need to be parallel,

00:04:03.020 --> 00:04:06.816
and all the sides have to be equal.

00:04:06.816 --> 00:04:09.500
So for example,

00:04:09.500 --> 00:04:12.810
this that I'm drawing,

00:04:12.810 --> 00:04:16.321
that is a parallelogram,
but it is not a rhombus.

00:04:16.321 --> 00:04:18.897
It's a parallelogram because that side,

00:04:18.897 --> 00:04:21.277
these opposite sides are parallel.

00:04:21.277 --> 00:04:24.598
If they kept going, they
would not cross each other.

00:04:24.598 --> 00:04:28.556
And these two opposite sides are parallel.

00:04:28.556 --> 00:04:30.355
So it's a parallelogram,
but it's not a rhombus

00:04:30.355 --> 00:04:34.621
because the blue sides are
longer than the yellow sides.

00:04:34.621 --> 00:04:36.746
So that is not a rhombus.

00:04:36.746 --> 00:04:39.985
A rhombus would have to look like this.

00:04:39.985 --> 00:04:42.608
A rhombus would have to look like that.

00:04:42.608 --> 00:04:44.384
So opposite sides are parallel

00:04:44.384 --> 00:04:47.182
and all the sides are the same length.

00:04:47.182 --> 00:04:50.584
And now you might say, "Well
maybe a square is a rhombus,"

00:04:50.584 --> 00:04:51.721
and I want you to think about that.

00:04:51.721 --> 00:04:53.762
Is a square a rhombus?

00:04:53.762 --> 00:04:56.156
Are all the sides the same length,

00:04:56.156 --> 00:04:58.942
and are the opposite sides parallel?

00:04:58.942 --> 00:05:00.820
Well we already said
that the opposite sides

00:05:00.820 --> 00:05:01.933
of a square are parallel.

00:05:01.933 --> 00:05:03.825
A square is a parallelogram.

00:05:03.825 --> 00:05:07.644
And all the sides of a
square are the same length.

00:05:07.644 --> 00:05:11.034
So a square is a rhombus.

00:05:11.034 --> 00:05:14.691
So one way to think about
rhombuses, or rhombi,

00:05:14.691 --> 00:05:16.479
is they're squares,

00:05:16.479 --> 00:05:18.610
and you could kind of view them as

00:05:18.610 --> 00:05:21.273
kind of a pushed over version of squares,

00:05:21.273 --> 00:05:22.399
if a square was moving

00:05:22.399 --> 00:05:24.698
really, really, really fast in a cartoon,

00:05:24.698 --> 00:05:28.774
that's what my brain thinks
of when I think of a rhombus.

00:05:28.774 --> 00:05:30.500
So now let's think of rectangle.

00:05:30.500 --> 00:05:32.775
And you might have heard the
word rectangle in the past,

00:05:32.775 --> 00:05:33.959
but let's think a little bit more

00:05:33.959 --> 00:05:36.293
about what makes a rectangle.

00:05:36.293 --> 00:05:39.810
So a rectangle is going
to be a parallelogram,

00:05:39.810 --> 00:05:42.736
but that by itself does
not make it a rectangle.

00:05:42.736 --> 00:05:46.523
So for example, this right
over here is a rectangle.

00:05:46.523 --> 00:05:47.373
Why is it?

00:05:47.373 --> 00:05:49.532
Well it's definitely a parallelogram.

00:05:49.532 --> 00:05:52.527
This side and that side are parallel.

00:05:52.527 --> 00:05:54.942
They'll never intersect.

00:05:54.942 --> 00:05:59.528
And this side and this side are parallel.

00:05:59.528 --> 00:06:01.826
They're never, they're
never going to intersect

00:06:01.826 --> 00:06:03.606
if you kept going on and on and on,

00:06:03.606 --> 00:06:07.286
or they're never going
to cross each other.

00:06:07.286 --> 00:06:09.620
But what makes it a rectangle?

00:06:09.620 --> 00:06:10.560
It's definitely a parallelogram,

00:06:10.560 --> 00:06:13.880
but what makes it, why do
we use the word rectangle?

00:06:13.880 --> 00:06:16.063
Well one way to think about it is

00:06:16.063 --> 00:06:19.058
they way that they come
together at the corners.

00:06:19.058 --> 00:06:22.343
So in a rectangle, the things come in to,

00:06:22.343 --> 00:06:24.642
I guess you could call
them square corners.

00:06:24.642 --> 00:06:26.963
And that's called a right angle.

00:06:26.963 --> 00:06:29.134
That's called a right
angle right over there.

00:06:29.134 --> 00:06:30.585
So this is what makes a rectangle.

00:06:30.585 --> 00:06:34.057
It's a parallelogram where all
the corners are right angles.

00:06:34.057 --> 00:06:35.902
You could put a little square there,

00:06:35.902 --> 00:06:37.702
if you wanna think about it that way.

00:06:37.702 --> 00:06:41.416
So for example, this right over here

00:06:41.416 --> 00:06:43.052
would not be a rectangle.

00:06:43.052 --> 00:06:43.444
Why?

00:06:43.444 --> 00:06:45.596
Cause you can't, if you
put a square here, notice.

00:06:45.596 --> 00:06:48.702
That does not, a square
doesn't fit in the corners

00:06:48.702 --> 00:06:50.957
the way that it fits right over here.

00:06:50.957 --> 00:06:55.067
That you have, the square
does not fit over here.

00:06:55.067 --> 00:06:57.806
This is a parallelogram,
but not a rectangle.

00:06:57.806 --> 00:07:02.149
A rectangle is a parallelogram
that has square corners.

00:07:02.149 --> 00:07:04.273
But what about our square?

00:07:04.273 --> 00:07:06.316
Is a square a rectangle?

00:07:06.316 --> 00:07:08.754
Well let's draw it out.

00:07:08.754 --> 00:07:09.397
Well let's think about it.

00:07:09.397 --> 00:07:11.661
A square, opposite sides are parallel.

00:07:11.661 --> 00:07:13.576
We've already said it's a parallelogram.

00:07:13.576 --> 00:07:16.919
And a square has,

00:07:16.919 --> 00:07:19.578
the corners are square.

00:07:19.578 --> 00:07:21.401
That's where when people
say make a square corner,

00:07:21.401 --> 00:07:22.711
that's where it comes from.

00:07:22.711 --> 00:07:24.059
The corners are square.

00:07:24.059 --> 00:07:25.580
They are at right angles.

00:07:25.580 --> 00:07:27.668
So the square is a rectangle.

00:07:27.668 --> 00:07:31.291
So the square is a really
interesting quadrilateral,

00:07:31.291 --> 00:07:35.355
because a square falls in
to all of these categories.

00:07:35.355 --> 00:07:38.337
The square, a square is a square,

00:07:38.337 --> 00:07:39.657
it's a rhombus,

00:07:39.657 --> 00:07:41.212
it's the type of rhombus

00:07:41.212 --> 00:07:44.805
where the corners are right angles,

00:07:44.805 --> 00:07:46.825
or you could say where
the corners are square.

00:07:46.825 --> 00:07:48.601
This one right over here is not a square,

00:07:48.601 --> 00:07:49.472
this one is square.

00:07:49.472 --> 00:07:52.107
They're both rhombuses,
or they're both rhombi.

00:07:52.107 --> 00:07:54.162
A square is also a rectangle.

00:07:54.162 --> 00:07:58.038
It's a parallelogram where
the corners are right angles,

00:07:58.038 --> 00:07:59.641
where they are square.

00:07:59.641 --> 00:08:01.637
A square is definitely a parallelogram,

00:08:01.637 --> 00:08:05.126
and everything we've talked
about is a quadrilateral.