🪞 Symmetry

Lines of symmetry — fold shapes in half perfectly! 🍭

📖 Learn
Lines of symmetry

✏️ Examples
Step-by-step

🔬 Visualiser
Grid mirror tool

🎯 Practice
20 mixed questions

🍰 Symmetry Fact!

Butterflies, leaves and human faces all have roughly one line of symmetry. Snowflakes have 6 lines of symmetry! The word "symmetry" comes from Greek meaning "same measure".

📖 Lines of Symmetry

1. What is a Line of Symmetry?

A line of symmetry (also called a mirror line) divides a shape into two parts that are exact mirror images of each other.

If you fold along the line, both halves match perfectly!

Think of it like a mirror: one side reflects to the other.

2. Directions of Symmetry Lines

Type	Description	Example shapes
Vertical	Line goes up and down (\|)	Square, rectangle, isosceles triangle
Horizontal	Line goes left and right (—)	Rectangle, square, rhombus
Diagonal	Line goes corner to corner (\\ or /)	Square, rhombus

3. Common Shapes and Their Lines of Symmetry

Shape	Lines of symmetry
Equilateral triangle	3
Isosceles triangle	1
Scalene triangle	0
Square	4
Rectangle	2
Rhombus	2
Regular pentagon	5
Regular hexagon	6
Circle	Infinite

4. Letters with Symmetry

Some capital letters have lines of symmetry:

Letter	Symmetry?	Type
A	Yes	Vertical
B	Yes	Horizontal
C	Yes	Horizontal
H	Yes	Both
I	Yes	Both
M	Yes	Vertical
O	Yes	Many
T	Yes	Vertical
J, N, S, Z	No	—

5. Regular Polygons Rule

A regular polygon with n sides always has n lines of symmetry.

Regular polygon: sides = lines of symmetry

Pentagon (5 sides) → 5 lines of symmetry

Hexagon (6 sides) → 6 lines of symmetry

Octagon (8 sides) → 8 lines of symmetry

6. Completing Symmetric Patterns

To complete a pattern on a grid:

Find the mirror line (axis of symmetry)

For each shaded square, count how far it is from the mirror line

Shade the matching square the same distance on the other side

✏️ Worked Examples

Example 1 – Lines of symmetry in a shape

How many lines of symmetry does a rectangle have?

Fold left to right: the halves match → 1 line

Fold top to bottom: the halves match → 1 line

Fold diagonally: halves do NOT match (unless it's a square)

Answer: 2 lines of symmetry

Example 2 – Letter symmetry

Does the letter A have a line of symmetry? (1=yes, 0=no)

Draw a vertical line down the middle of A

The left side mirrors the right side

Answer: 1 (Yes)

Example 3 – Regular polygon symmetry

How many lines of symmetry does a regular hexagon have?

A regular hexagon has 6 sides

Regular polygon: lines of symmetry = number of sides

Answer: 6

Example 4 – Grid symmetry

3 squares are shaded on the left of a mirror line. How many match on the right?

Each shaded square has exactly one mirror square

3 shaded → 3 matching squares needed

Answer: 3 squares

Example 5 – Identify lines from description

A square: how many lines of symmetry?

Vertical (|), Horizontal (—), Diagonal (\), Diagonal (/)

Answer: 4

🔬 Grid Mirror Tool

Click squares in the left half (columns 1–4) to shade them. The right half auto-mirrors! Toggle the axis to switch between vertical and horizontal symmetry.

Symmetry Grid (8 × 8)

Click squares on the left half to draw!

Symmetry Checker

How many lines of symmetry does this shape have?