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[silence]

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So I heard you didn't really

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get the transformations,

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but I think I can help you

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out a little bit.

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So, transform just means

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change something.

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You already know that.

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And in geometry,

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there are some
types of transformations

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that are helpful to know about.

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So, the main thing is

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you have a first thing

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and then a second thing.

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So, one shape changes

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into another shape.

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And, the first one's called

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the pre-image,

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and the next one's
called the image.

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So, "pre" just means before.

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Just remember that,

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like pre-liminary and
pre-historic

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and then the next image.

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So, the first kind

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is a reflection.

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And again, you know what
this means already,

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but a reflection in geometry

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just means that

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you've flipped something

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over an axis.

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So, you could even look

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at your hands.

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This hand is a reflection
of the other hand.

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So, they've just flipped
onto each other,

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or you could think about a

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um, like a landscape scene.

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If you look at a lake

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that's reflecting,

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like the mountains,

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then it's just,

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the axis is that line

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of where the lake starts.

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So, that's a good way
to remember.

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Another kind
is called a rotation,

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and you know what that is too.

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But a rotation just means

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you're switching a shape

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onto a rotating axis.

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So, like this.

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And, another way to think

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about a rotation

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is two reflections.

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And, that doesn't need

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to be confusing.

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All you need to know is that

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if you have one thing

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reflected onto another

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and then it reflects again,

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it ends up being a rotation.

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So...

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That's a good way to
remember that too.

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And, one more type

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is called a translation.

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So, this is just like a slide.

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So, just like this

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moving over here.

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That's a translation.

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Another way to think

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about a translation is again,

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two reflections,

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but this time the reflections

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are in a straight line.

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So, if you reflect
this hand...here

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and you reflect it
one more time,

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then this hand

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has reflected over here.

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So, sorry

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this hand has translated
over here.

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So, these types, um,

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of transformations
are called isometric.

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A translation, a rotation,
and a reflection

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are all
isometric transformations.

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That just means same.

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So, when you start out

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with a pre-image,

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it will always be the same size

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and shape as the image.

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But, there's one more type

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of transformation

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that isn't isometric,

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and that's called dilation.

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And, if you ever go

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to the eye doctor,

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and they dilate your eyes,

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it means they made them

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really big so that they could

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see inside them.

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So, when you dilate a shape,

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you make it either

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smaller or bigger,

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one of those two.

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So, one more term

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is a glide reflection.

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And a glide reflection

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is exactly what it sounds like.

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It's just one reflection

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plus one translation,

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and these can be
in either order.

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You could either
translate and then reflect

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or you could 
reflect and then translate.

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Either way.

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[pause]

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So, transformations are helpful,

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because we can know about

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something called a tessellation.

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And a tessellation is

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just a repeating shape,

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but only certain types
of shapes can repeat

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in patterns that don't overlap.

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So, if we had like

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a crazy star or something,

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it wouldn't tessellate,

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because it's a weird shape.

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But, if we had just like
a square or a rectangle,

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it'll tessellate perfectly,

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because they can overlap

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in any sort of pattern.

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So like, it's why we can have

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a brick wall or something,

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you know.

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They can...

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they perfectly fit
next to each other

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and on top of each other.

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But, if you need to know

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what types of shapes
can tessellate,

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we can remember
by angle measure.

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So, if all the angles of a shape

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equal 360 degrees,

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then they'll be able
to tessellate.

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So, sometimes you can look

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at a shape and figure it out.

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Other times, maybe you can't.

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So, if you need to remember

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what types of shapes can,

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if all the angles that meet up

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equal 360,

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then you're in business.

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You can tessellate.

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So, you know rectangles can,

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like in this picture.

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But then in the next one,

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we have two different shapes.

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We have squares and triangles,

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and you can see that

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all these angles together,

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the 90 plus 90 plus
60 plus 60 plus 60

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equals 360 degrees.

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And, if you just add up

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all the angles that touch

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and they equal 360,

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then you can see,

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like right here,

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that they tessellate perfectly.