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What Is Mirror Symmetry in Maths?

Imagine you’re looking at yourself in the mirror. On the other side of the mirror there’s another version of you that is just like you, except it’s mirrored. That’s what we call mirror symmetry.

The math master looking at her reflection in a mirror

The math master looking at her reflection in a mirror

But how does mirror symmetry work when we’re talking about geometric figures? There are two ways to look at it. The first one is when the mirror is on the outside of the figure. It’s as if the figure is looking at itself in the mirror. In a symmetry drawing, the mirror is represented by a line. We call this line the line of symmetry.

Two triangles and line of symmetry

The other way to look at it is when the mirror is on top of the figure. The mirror is again represented by the line we call the line of symmetry.

Heart and the letter E with symmetry lines

Some figures have several lines of symmetry. That happens when the figure can be mirrored across several lines.

Square and triangle with symmetry lines

Some figures have no lines of symmetry. That happens when they can’t be mirrored across any lines.

The letter L and a teacup

Think About This

Can you draw figures with one, more than one, or no lines of symmetry?

Try the letters E, B, V, H and I.

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