Symmetry meaning in maths

Something is symmetrical when it has two matching halves. You can check for symmetry in shape by drawing a mirror line down the middle and seeing if both halves are identical.

In other words, symmetry exists when something with matching parts faces each other or around an axis.

But what makes a shape symmetrical? Put, symmetrical (or symmetric) shapes have one side that is the same as the other. Symmetrical shapes look the same after being reflected, rotated, or translated.

Lines of symmetry meaning

A line of symmetry splits a shape in half, creating two identical shapes. When drawing this line, you need to find the exact middle of a shape or figure.

Above are two examples of symmetrical shapes and their lines of symmetry. It’s also important to note that some shapes can have multiple lines of symmetry. Take a square, for example – you can draw four lines of symmetry on a square—one horizontally across the middle, one vertically down the middle, and two going diagonally each way.

A line of symmetry can also be called a ‘mirror line’ as a mirror can be placed along it, and the reflection would show the entire shape. Small mirrors can be handy in the classroom to help children understand the meaning of symmetry and how it works.

Different types of symmetry: meaning

Now that we’ve established reflectional (or line) symmetry let’s look at the other main ways a shape or pattern can be deemed symmetrical. While students may not learn about these until high school, it’s worth knowing the basics of these other forms of symmetry in maths.

What are the four types of symmetry?

The four types of symmetry are rotational, translational, reflection, and glide reflection.

Rotational symmetry

They are also known as radial symmetry. A shape or pattern has rotational symmetry when it looks the same after being rotated less than one complete turn. We count rotational symmetry by the number of turns it takes for a shape to look the same. This is called the ‘order’ of rotational symmetry. For example, a rectangle has an order of 2, and a five-point star has an order of 5.

Translational symmetry

Translational symmetry in maths is slightly more complex and is only introduced in high school. For an object to have translational symmetry, it needs to have been translated or cloned and moved in a specific direction and at a certain distance away. There must be more than one of a particular pattern or object for it to have translational symmetry, which is why it’s often helpful to think of a repeated pattern as an example of translational symmetry.

If you had a border of small square shapes across the top of a wall in your home, you’d want these to be repeated at the same distance. This would be an example of translational symmetry.

Glide reflection symmetry

Glide reflection symmetry is best described as a hybrid between reflection and translational symmetry. It involves both processes, but in a specific order; review over a line and translation along the line. A shape must first be reflected and then translated in any direction for glide reflection to have taken place.

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