Symmetry: Fold, Reflect and Rotate
Explore lines of symmetry, mirror halves, paper folding, rotational symmetry, angles of rotation and repeating designs found in rangoli, butterflies, flowers, pinwheels and architecture.
Fact Sheet: Big Ideas
Symmetry means that a part or parts of a figure repeat in a definite pattern. A cloud usually has no fixed repeated pattern, while a butterfly, rangoli, pinwheel or flower may show symmetry.
Line of Symmetry
A line that cuts a figure into two parts that exactly overlap when folded.
mirror halvesfold lineReflection Symmetry
One side of the figure reflects to the other side across a line.
left ↔ righttop ↔ bottomRotational Symmetry
A figure has rotational symmetry when it looks exactly the same after some turn less than a full turn.
centre of rotationangle of symmetryAlways true
Every figure matches itself after a 360° turn. We count rotational symmetry only when there are matching turns before 360° too.
360° full turn| Figure | Lines of symmetry | Angles of rotational symmetry |
|---|---|---|
| Square | 4 | 90°, 180°, 270°, 360° |
| Equilateral triangle | 3 | 120°, 240°, 360° |
| Regular hexagon | 6 | 60°, 120°, 180°, 240°, 300°, 360° |
| Windmill with 4 equal arms | May have none | 90°, 180°, 270°, 360° |
| Ordinary cloud | Usually none | Usually none |
Classroom connection
Paper folding, ink blots, paper cutting and punched holes make symmetry visible because the fold becomes the line of symmetry.
Reflection Lab: Complete the Mirror Image
Choose a mirror line
See how a point and a polygon reflect across a vertical, horizontal or diagonal line.
Reflection canvas
Think
When a figure is reflected, the original and image are at equal distances from the mirror line, but on opposite sides.
Rotation Lab: How many turns match?
Radial arms explorer
Rotating figure
| Equal arms | Smallest matching turn | All angles of symmetry |
|---|---|---|
| 3 | 120° | 120°, 240°, 360° |
| 4 | 90° | 90°, 180°, 270°, 360° |
| 5 | 72° | 72°, 144°, 216°, 288°, 360° |
| 6 | 60° | 60°, 120°, 180°, 240°, 300°, 360° |
Pattern Studio
Make a paper-cut preview
Select a fold and a cut style. The lab shows the unfolded symmetric shape.
Unfolded pattern
Design challenge
Create a kolam, rangoli, logo or border pattern with exactly 1, 2, 3, 4 or 6 lines of symmetry. Then ask a partner to identify all mirror lines and rotational turns.
Activity Zone
Quick exploration prompts
Worksheet Generator
Create a printable worksheet for practice on lines of symmetry, reflection, rotational symmetry and paper folding.
Teacher Tools
Learning Goals
- Identify lines of symmetry by folding or visual reasoning.
- Complete mirror images on grid paper.
- Distinguish reflection symmetry from rotational symmetry.
- Find angles of rotational symmetry for radial patterns.
Misconceptions to watch
- Thinking every balanced-looking figure has a line of symmetry.
- Counting 360° alone as “rotational symmetry”.
- Missing diagonal symmetry in a square.
- Assuming a rectangle’s diagonal is a line of symmetry.
Hands-on materials
- Square paper, scissors, hole punch.
- Transparent sheet for reflection checks.
- Cut-out windmills or radial arms.
- Dot grid and squared paper.
Exit ticket
Ask students to draw one figure with exactly two lines of symmetry and another with rotational symmetry but no line of symmetry.