Mirror lines and turning shapes. Read a little, then play. Clear all six games!
What it is
A line of symmetry is a fold line: if you fold the shape along it, the two halves match exactly, like a mirror.
Why it works
Each half is the mirror image of the other across that line, so every point on one side has a matching point the same distance on the other side.
Why it matters
Symmetry is all around us, in leaves, faces, buildings and rangoli, and knowing it helps in art and design.
A few examples
A square has 4 lines of symmetry. An equilateral triangle has 3. A rectangle has 2.
What it is
Many letters and shapes have a vertical mirror line down the middle, so the left half is the mirror image of the right.
Why it works
Fold the letter down the middle: if the two halves land exactly on each other, it has a vertical line of symmetry. Letters like A, H, M, T, U, V, W, X, Y do.
Why it matters
Spotting mirror lines trains your eye and helps in design, typography and puzzles.
A few examples
A, H, O and X have a vertical mirror line. F, G, J and P do not.
What it is
Some letters have a line of symmetry and some have none. A few have more than one.
Why it works
You test by folding: if a fold makes the halves match, that fold is a line of symmetry. Letters like S, N, Z and P have none, while H, O and X have two.
Why it matters
Sorting things by symmetry is a neat way to see hidden patterns.
A few examples
H and X have symmetry. S, N and Z have none.
What it is
A shape has rotational symmetry if it looks exactly the same after turning it part of a full circle. The order is how many times it matches in one full turn.
Why it works
Turn the shape slowly through 360 degrees and count how many positions look identical to the start. A square matches 4 times, so its order is 4.
Why it matters
Rotational symmetry appears in wheels, flowers, fans and logos.
A few examples
A square has order 4. An equilateral triangle has order 3. A rectangle has order 2.
What it is
A regular polygon has all sides and all angles equal. A regular polygon with N sides has exactly N lines of symmetry and rotational symmetry of order N.
Why it works
Each line of symmetry passes through a corner and the middle of the opposite side (or two opposite corners), and there is one for each side, so N sides give N lines.
Why it matters
This neat rule lets you find the symmetry of any regular shape instantly.
A few examples
A regular pentagon (5 sides) has 5 lines. A regular hexagon (6 sides) has 6.
What it is
To check if a line is a line of symmetry, imagine folding along it. It is a line of symmetry only if the two halves match exactly.
Why it works
A rectangle folds to matching halves along its two midlines, but NOT along a diagonal, because the diagonal halves do not sit on top of each other.
Why it matters
Testing folds is the surest way to decide whether a line really is a line of symmetry.
A few examples
A rectangle folded along the middle matches. A rectangle folded along a diagonal does not.
Have a go on paper first, then tap to see the clear steps.
Q1. How many lines of symmetry does a square have?
Q2. Does the letter H have a vertical line of symmetry?
Q3. What is the order of rotational symmetry of an equilateral triangle?
Q4. How many lines of symmetry does a regular hexagon have?
Q5. Is a diagonal of a rectangle a line of symmetry?
Q6. How many lines of symmetry does a rectangle (not a square) have?