Learning About Shapes

Long ago, people in Greece studied shapes.
They learned a lot about them.
Other people helped too.
People from Egypt helped.
People from Babylon helped.

A man named Euclid wrote it all down.
He made rules for shapes.
He used a straight edge.
He used a compass.
A compass helps draw circles.

Euclid had some starting rules.
He called them "self-evident."
That means everyone can see they are true.
He used these rules to prove new things.

One rule was tricky.
It was about parallel lines.
Parallel lines are lines that never touch.
It is hard to know if two lines will ever touch.
People argued about this for a very long time!

Later, people found new kinds of shapes and spaces.
Some spaces make all lines meet.
Some spaces keep lines apart.
A man named Felix Klein had a new idea.

Klein said: let's move shapes!
We can slide a shape.
We can flip a shape.
We can turn a shape.
These moves are called transformations.

Moving Shapes

When we move a shape without changing it, that is a rigid motion.
A rigid motion keeps the shape the same size.
It keeps the lines the same length.
It keeps the angles the same.

There are three kinds of rigid motions.
One is a slide. We call this a translation.
One is a flip. We call this a reflection.
One is a turn. We call this a rotation.

If we can slide, flip, or turn one shape onto another, they match.
We call matching shapes congruent.
Congruent shapes are the same size.
Congruent shapes are the same shape too.

Changing Size

Sometimes we make a shape bigger or smaller.
This is called a dilation.
A dilation keeps the angles the same.
But it changes how long the lines are.

If two shapes have the same shape, but not the same size, we call them similar.
We can turn one shape into a similar shape.
We slide, flip, turn, and change its size.

Look at the Pictures!

Look at Figure A.
All the shapes are the same size.
All the shapes are the same shape.
You can slide, flip, or turn one to make it match another.

Look at Figure B.
The shapes are the same shape.
But they are not the same size.

Look at Figures C and D.
These shapes are not the same size.
They are not the same shape either.

Some Simple Shape Facts

1. Two points make one line.
2. Two lines can be the same line.

Or they cross at one point.
Or they never cross at all.

1. Two circles might not touch.

They might touch at one point.
They might touch at two points.

1. Lines that never cross are called parallel.

Lines that cross and make matching square corners are called perpendicular.

1. In a triangle, two sides together are always longer than the third side.

What We Learn This Year

This year, we will slide, flip, and turn shapes.
We will make shapes bigger and smaller.
We will see which shapes match.
We will see which shapes are just alike in shape.

We will draw pictures of shapes.
We will move shapes with our hands.
We will use tools to help us.

This is how we start learning about shapes.
Later, we will learn even more!