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Academy11+

11+ Maths · Topic explained

Symmetry, reflection and rotation

Why does a butterfly look the same on both sides?

The big idea

A reflection flips a shape over a mirror line; a rotation turns it round a point.

Picture it

Like folding a painted butterfly: both halves match exactly.

Key words

line of symmetry
A fold line where both halves match exactly.
reflection
A mirror image: each point the same distance on the other side.
rotation
A turn about a fixed point, e.g. 90° clockwise.
order of rotational symmetry
How many times it looks the same in one full turn.

Worked examples

  1. 1Warm-up

    How many lines of symmetry does a rectangle have?

    • Fold top to bottom: it matches
    • Fold side to side: it matches
    • The diagonals don't work: 2 lines
  2. 211+ standard

    Reflect the shape in the mirror line.

    • Count squares from each corner to the mirror
    • Count the same number on the other side
  3. 311+ standard

    Rotate the shape 90° clockwise about the dot.

    • A quarter turn, the way clock hands go
    • Every square stays the same distance from the dot
  4. 411+ standard

    A regular hexagon: how many lines of symmetry? What order of rotational symmetry?

    • 6 lines of symmetry
    • It looks the same 6 times in a full turn: order 6

The common mistake

The mistake

A rectangle's diagonals are lines of symmetry.

Instead

They aren't: fold a rectangle along a diagonal and the corners don't meet.

Why: Try it with a piece of paper: the two halves don't sit on top of each other.

Where it comes up in the 11+

Count lines of symmetry, complete symmetric patterns, reflect or rotate shapes on a grid.

The video

Video coming soon

We're making a short video that explains symmetry, reflection and rotation step by step. Until then, everything it covers is on this page.

Free printable

Symmetry, reflection and rotation worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. How many lines of symmetry does a square have?

    • 2
    • 4
    • 1
    • 8
    Show the answer

    4

    Across, down, and both diagonals.

  2. 2. What is the order of rotational symmetry of an equilateral triangle?

    • 1
    • 2
    • 3
    • 6
    Show the answer

    3

    It looks the same 3 times in a full turn: every 120°.

  3. 3. How many lines of symmetry does the capital letter H have?

    • 0
    • 1
    • 2
    • 4
    Show the answer

    2

    One down the middle and one across the middle.