Symmetry & Transformation
Explore line symmetry, reflections and rotations to understand how shapes can be moved and flipped.
Line Symmetry
A shape has line symmetry if you can draw a line through it so that both halves are mirror images of each other. This line is called the line of symmetry (or axis of symmetry).
Lines of Symmetry in Common Shapes
Square
4 lines
Circle
Infinite lines
Rectangle
2 lines
Equilateral Triangle
3 lines
Tip: To check for symmetry, imagine folding the shape along the line. If both halves match exactly, it has line symmetry.
Reflection
A reflection flips a shape over a line (called the mirror line). The reflected shape is the same size and shape, but it faces the opposite direction — like looking in a mirror.
Reflecting a Shape
The blue shape is reflected in the mirror line to create the green shape.
Each point is the same distance from the mirror line on both sides.
Rotation
A rotation turns a shape around a fixed point. We describe rotations by the angle of turn (quarter turn = 90°, half turn = 180°, full turn = 360°) and the direction (clockwise or anticlockwise).
Rotation Examples
Original
90° clockwise
180°
270° clockwise
The shape stays the same size, but its orientation (which way it faces) changes.
Key Vocabulary
Line of Symmetry
A line that divides a shape into two identical mirror halves.
Reflection
A transformation that flips a shape over a mirror line.
Rotation
A transformation that turns a shape around a fixed point by a certain angle.
Transformation
A way of changing the position or orientation of a shape (reflection, rotation, translation).
Worked Examples
How many lines of symmetry does a regular hexagon have?
Step 1: A regular hexagon has 6 equal sides.
Step 2: A regular polygon has as many lines of symmetry as it has sides.
Answer: A regular hexagon has 6 lines of symmetry.
Describe the transformation that turns a shape upside down.
Step 1: Turning something upside down means it rotates halfway around.
Step 2: A half turn = 180°.
Answer: It is a rotation of 180°.
Does the letter B have a horizontal line of symmetry?
Step 1: Imagine drawing a horizontal line through the middle of B.
Step 2: The top half and bottom half look the same (both have bumps).
Answer: Yes, the letter B has a horizontal line of symmetry.
Knowledge Check
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Key Concepts Summary
- ●A line of symmetry divides a shape into two matching halves.
- ●A reflection flips a shape over a mirror line. The shape stays the same size.
- ●A rotation turns a shape around a fixed point by a certain angle.
- ●Quarter turn = 90°, half turn = 180°, three-quarter turn = 270°, full turn = 360°.
- ●Regular shapes have as many lines of symmetry as they have sides.