Symmetry & Reflection
Finding lines of symmetry, completing symmetrical figures and reflecting shapes in a mirror line.
What is Symmetry & Reflection?
Symmetry means a shape looks the same on both sides of a line (line symmetry) or looks the same after being rotated (rotational symmetry). Reflection means creating a mirror image of a shape across a line.
In the 11+ exam, you may be asked to find lines of symmetry, complete a symmetrical figure, reflect a shape in a mirror line, or identify the order of rotational symmetry.
Step-by-Step Method
For line symmetry, fold mentally
Imagine folding the shape along the line. If both halves match exactly, it is a line of symmetry.
For completing a symmetrical figure
Each point on the shape must have a matching point the same distance on the other side of the mirror line.
For reflection, use the perpendicular distance
Each point reflects to the same distance on the other side of the mirror line, measured at right angles to the line.
For rotational symmetry, rotate the shape
How many times does the shape look the same in one full turn? That number is the order of rotational symmetry.
Check each point carefully
Count squares from each point to the mirror line, then count the same number on the other side.
Worked Examples
How many lines of symmetry does an equilateral triangle have?
Working
- An equilateral triangle has 3 equal sides and 3 equal angles.
- Each line of symmetry goes from a vertex to the middle of the opposite side.
- There are 3 such lines.
What is the order of rotational symmetry of a regular pentagon?
Working
- A regular pentagon has 5 equal sides and 5 equal angles.
- It looks the same 5 times during a full rotation.
A point is 3 squares to the left of a vertical mirror line. Where is its reflection?
Working
- The reflection is the same distance on the OTHER side of the mirror line.
- 3 squares to the RIGHT of the mirror line.
Common Mistakes
Drawing too many lines of symmetry (e.g. 4 for a rectangle when there are only 2).
A rectangle has 2 lines of symmetry (horizontal and vertical). The diagonals are NOT lines of symmetry.
Reflecting at the wrong distance from the mirror line.
Count the distance carefully. Each point must be the SAME distance from the line on both sides.
Confusing reflection with rotation.
Reflection flips a shape (like a mirror). Rotation turns it (like a wheel).
Top Tips
- Use a mirror or tracing paper to check reflections if you are unsure.
- Regular polygons: number of lines of symmetry = number of sides.
- A shape with no rotational symmetry has order 1 (it only looks the same after a full 360-degree turn).
- When reflecting on a grid, count squares from each corner to the mirror line, then the same number on the other side.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions