GCSE-readySymmetry and properties of 2-D shapes
Every shape has its own properties: equal sides, parallel sides, right angles and symmetry. Knowing them helps you name shapes and solve angle problems.
Line and rotational symmetry
The order of rotational symmetry is how many times a shape looks the same in one full turn.
A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
A parallelogram (that is not a rectangle or rhombus) has no lines of symmetry but rotational symmetry of order 2.
Quadrilaterals
| Shape | Sides | Diagonals | Lines of symmetry | Rotation order |
|---|---|---|---|---|
| Square | 4 equal, 2 pairs parallel | Equal, cross at 90° | 4 | 4 |
| Rectangle | 2 pairs equal and parallel | Equal | 2 | 2 |
| Rhombus | 4 equal, 2 pairs parallel | Cross at 90° | 2 | 2 |
| Parallelogram | 2 pairs equal and parallel | Bisect each other | 0 | 2 |
| Kite | 2 pairs of equal adjacent sides | Cross at 90° | 1 | 1 |
| Trapezium | Exactly 1 pair parallel | Not usually special | 0 (1 if isosceles) | 1 |
Triangles and notation
Isosceles: 2 equal sides and 2 equal base angles, 1 line of symmetry.
Scalene: no equal sides or angles.
On diagrams, matching dashes show equal sides and matching arrows show parallel lines.
A quadrilateral has four equal sides, but its angles are not right angles. Name it and describe its symmetry.
- Four equal sides: square or rhombus
- Not right angles, so not a square
- A rhombus has 2 lines of symmetry and order 2
Answer: Rhombus: 2 lines of symmetry, rotational symmetry of order 2
Regular n-sided polygons have n lines of symmetry and order n. Learn the quadrilateral family by sides, angles, diagonals and symmetry.
- Parallel
- Lines that are always the same distance apart and never meet.
- Polygon
- A flat shape with straight sides, such as a pentagon (5 sides) or hexagon (6 sides).
- Parallel lines
- Alternate angles are equal. Corresponding angles are equal. Co-interior angles add to 180°.
- Not “Parallelogram”. A parallelogram has two pairs of parallel sides.
- Not “Kite”. A kite has no parallel sides.
- Not “Square”. A square has 4 lines of symmetry.
- Not “Rhombus”. A rhombus has 2 lines of symmetry.
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2 more questions
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How many lines of symmetry does a regular pentagon have?
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Answer: 5
A regular pentagon has 5 lines of symmetry: one through each vertex and the middle of the opposite side.
What is the order of rotational symmetry of a regular pentagon?
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Answer: 5
It fits onto itself 5 times in a full turn.
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Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.