[silence]
So I heard you didn't really
get the transformations,
but I think I can help you
out a little bit.
So, transform just means
change something.
You already know that.
And in geometry,
there are some types of transformations
that are helpful to know about.
So, the main thing is
you have a first thing
and then a second thing.
So, one shape changes
into another shape.
And, the first one's called
the pre-image,
and the next one's called the image.
So, "pre" just means before.
Just remember that,
like pre-liminary and pre-historic
and then the next image.
So, the first kind
is a reflection.
And again, you know what this means already,
but a reflection in geometry
just means that
you've flipped something
over an axis.
So, you could even look
at your hands.
This hand is a reflection of the other hand.
So, they've just flipped onto each other,
or you could think about a
um, like a landscape scene.
If you look at a lake
that's reflecting,
like the mountains,
then it's just,
the axis is that line
of where the lake starts.
So, that's a good way to remember.
Another kind is called a rotation,
and you know what that is too.
But a rotation just means
you're switching a shape
onto a rotating axis.
So, like this.
And, another way to think
about a rotation
is two reflections.
And, that doesn't need
to be confusing.
All you need to know is that
if you have one thing
reflected onto another
and then it reflects again,
it ends up being a rotation.
So...
That's a good way to remember that too.
And, one more type
is called a translation.
So, this is just like a slide.
So, just like this
moving over here.
That's a translation.
Another way to think
about a translation is again,
two reflections,
but this time the reflections
are in a straight line.
So, if you reflect this hand...here
and you reflect it one more time,
then this hand
has reflected over here.
So, sorry
this hand has translated over here.
So, these types, um,
of transformations are called isometric.
A translation, a rotation, and a reflection
are all isometric transformations.
That just means same.
So, when you start out
with a pre-image,
it will always be the same size
and shape as the image.
But, there's one more type
of transformation
that isn't isometric,
and that's called dilation.
And, if you ever go
to the eye doctor,
and they dilate your eyes,
it means they made them
really big so that they could
see inside them.
So, when you dilate a shape,
you make it either
smaller or bigger,
one of those two.
So, one more term
is a glide reflection.
And a glide reflection
is exactly what it sounds like.
It's just one reflection
plus one translation,
and these can be in either order.
You could either translate and then reflect
or you could reflect and then translate.
Either way.
[pause]
So, transformations are helpful,
because we can know about
something called a tessellation.
And a tessellation is
just a repeating shape,
but only certain types of shapes can repeat
in patterns that don't overlap.
So, if we had like
a crazy star or something,
it wouldn't tessellate,
because it's a weird shape.
But, if we had just like a square or a rectangle,
it'll tessellate perfectly,
because they can overlap
in any sort of pattern.
So like, it's why we can have
a brick wall or something,
you know.
They can...
they perfectly fit next to each other
and on top of each other.
But, if you need to know
what types of shapes can tessellate,
we can remember by angle measure.
So, if all the angles of a shape
equal 360 degrees,
then they'll be able to tessellate.
So, sometimes you can look
at a shape and figure it out.
Other times, maybe you can't.
So, if you need to remember
what types of shapes can,
if all the angles that meet up
equal 360,
then you're in business.
You can tessellate.
So, you know rectangles can,
like in this picture.
But then in the next one,
we have two different shapes.
We have squares and triangles,
and you can see that
all these angles together,
the 90 plus 90 plus 60 plus 60 plus 60
equals 360 degrees.
And, if you just add up
all the angles that touch
and they equal 360,
then you can see,
like right here,
that they tessellate perfectly.