# Transformations and SymmetrySymmetry

**Symmetry***the same* in some way. But using transformations, we can give a much more precise, mathematical definition of what symmetry *really* means:

An object is *symmetric* if it looks the same, even after applying a certain transformation.

We can reflect this butterfly, and it looks the same afterwards. We say that it has **reflectional symmetry**.

We can rotate this flower, and it looks the same afterwards. We say that it has **rotational symmetry**.

## Reflectional Symmetry

A shape has **reflectional symmetry****axis of symmetry**

Draw all axes of symmetry in these six images and shapes:

Many letters in the alphabet have reflectional symmetry. Select all the ones that do:

Here are some more shapes. Complete them so that they have reflectional symmetry:

Shapes, letters and images can have reflectional symmetry, but so can entire numbers, words and sentences!

For example “25352” and “ANNA” both read the same from back to front. Numbers or words like this are called **Palindromes**

If we ignore spaces and punctuation, these letters also have reflectional symmetry. Can you come up with your own?

Never odd or even.

A

Yo, banana

But Palindromes are not just fun, they actually have practical importance. A few years ago, scientists discovered that parts of our

## Rotational Symmetry

A shape has **rotational symmetry**

The **order of symmetry***number of times we can rotate the shape*, before we get back to the start. For example, this snowflake has order

The angle of each rotation is

Find the order and the angle of rotation, for each of these shapes:

Now complete these shapes, so that they have rotational symmetry: