Symmetry

Symmetry

Get ready to become a symmetry detective! Symmetry is hiding everywhere — in butterflies, snowflakes, football badges, even your own face. Once you can spot it, those Non-Verbal Reasoning questions turn into quick, easy marks. Let's go!

There are two types of symmetry to master:

1. Line symmetry — the mirror kind
2. Rotational symmetry — the spinning kind

Line Symmetry: The Mirror Test

A shape has line symmetry if you can draw a straight line through it so that one half is a perfect mirror image of the other. That line is called the line of symmetry (or the mirror line).

Here's the easiest test ever: imagine folding the shape along the line, like folding a piece of paper. If the two halves land exactly on top of each other — snap! — it's a line of symmetry.

The shape on the left folds in half perfectly, so it's symmetrical. The wonky shape on the right just won't match, however you fold it — so it has no line of symmetry.

Did you know? A butterfly is a perfect example of line symmetry — its left wing is a mirror image of its right wing. So is (almost!) every human face.

How Many Lines Can a Shape Have?

Some shapes are real show-offs and have lots of lines of symmetry! Here's a handy rule: a regular shape (all sides and angles equal) has the same number of lines of symmetry as it has sides. A square has 4 sides, so it has 4 lines. Neat!

Pop these into your memory bank:

• Equilateral triangle → 3 lines
• Square → 4 lines
• Rectangle → 2 lines (just up–down and left–right — the diagonals are sneaky imposters!)
• Regular pentagon → 5 lines
• Regular hexagon → 6 lines
• Circle → infinitely many!

Tricky trap! A rectangle is not a square. If you fold a rectangle along its diagonal, the corners miss each other — so a diagonal is not a line of symmetry.

Mirror Lines Love to Tilt

A line of symmetry doesn't have to go straight up and down. It can be vertical, horizontal, or diagonal — and some shapes have lines pointing every which way!

Top exam tip: Lots of pupils check only for an up-and-down mirror line and miss the rest. Always look sideways and diagonally too. Stuck on a diagonal one? Tilt your head (or turn the page) so it becomes vertical — much easier to spot!

Rotational Symmetry: The Spin

Time to spin! A shape has rotational symmetry if it looks exactly the same after you turn it part of the way around — without flipping it over.

The order of rotational symmetry is just a clever way of asking: how many times does it look the same in one full spin?

• A square looks the same 4 times as it spins all the way round → order 4 (a quarter turn each time).
• An equilateral triangle → order 3.
• The pinwheel spins to look the same 3 times too → order 3 — but look closely: it has no mirror line at all! A shape can spin-match without being a mirror-match.

Spot it in real life: A fidget spinner is usually order 3. So is the recycling symbol! Many car wheel hubcaps are order 5.

In the Exam

Symmetry questions usually turn up in these styles:

• Which shape has a line of symmetry? → use the fold test on each option.
• How many lines of symmetry? → count carefully: up–down, side–side and diagonal.
• Complete the symmetrical figure → reflect the pattern across the mirror line.
• Which is the mirror image? → the answer is flipped, not turned.

Your Turn: Complete the Pattern

The left half of this pattern is given, with a mirror line down the middle. To finish it, reflect every shaded square across the line — pretend the line really is a mirror!

The trick: a square 1 step to the left of the line needs a partner 1 step to the right. A square 3 steps away matches one 3 steps away on the other side. Count the steps, copy it across — and you'll get it right every time.

Quick Recap

• Line symmetry: one half mirrors the other — use the fold test.
• Count all the lines: vertical, horizontal and diagonal.
• A regular shape has as many lines of symmetry as it has sides.
• Rotational symmetry: it matches itself as it spins; the order = how many times in one full turn.
• For "complete the figure": count each square's steps from the mirror line and copy them across.

You're now a fully qualified symmetry detective! Go and try the exercises — you've got this!