Chapter 11: Fun with Symmetry

A butterfly's wings, a peacock's feathers, the Taj Mahal , they all share a secret. Their two halves match like reflections in a mirror. That's symmetry!

What we'll learn

• What symmetry means.
• How to find a line of symmetry.
• Identify shapes with one, two or many lines of symmetry.
• Create symmetric designs.

The big idea

A shape is symmetric if you can fold it along a line so that both halves match perfectly. That fold line is called the line of symmetry or axis of symmetry.

A square has 4 lines of symmetry , fold it down the middle horizontally, vertically, or diagonally. A rectangle has 2 (horizontal and vertical), not the diagonals. An equilateral triangle has 3.

A circle is the champion of symmetry. It has infinite lines of symmetry , fold it through the centre at any angle, and both halves match.

The letter A is symmetric. So is M. But the letter F is not symmetric.

Symmetry is everywhere , in flowers, faces, footprints and ironwork on gates. We can use a small mirror to test: place the mirror on a shape; if the reflection completes the shape, the mirror line is a line of symmetry.

Explore with examples

1. How many lines of symmetry does a square have?

4 , 1 vertical, 1 horizontal, 2 diagonal.

2. Is the letter B symmetric? Find its line.

Yes. The line of symmetry is horizontal, through the middle.

3. Is the digit 8 symmetric?

Yes , horizontally and vertically. So 2 lines.

4. Draw a butterfly using symmetry.

Fold a paper in half. Draw half a butterfly along the fold. Cut along the outline. Open , a perfect symmetric butterfly!

Hands-on activities

Inkblot Magic

Drop a blob of paint on one half of a folded sheet of paper. Close the sheet, press gently and open. The two halves are mirror images , symmetric!

Mirror Check

Place a small mirror upright along any line of a shape. If the reflection completes the shape, that line is symmetric. Test it on a square, a rectangle, and your name written in capitals.

Rangoli Designer

On dotted paper, draw half of a rangoli. Now mirror it on the other half. Use colours to fill it in. Symmetric beauty!

Try it yourself

1. How many lines of symmetry does an equilateral triangle have?
2. Is the letter H symmetric? How many lines?
3. Name 3 things in nature that are symmetric.
4. Draw a heart shape. How many lines of symmetry?
5. Which has more lines of symmetry: a rectangle or a square?
6. Write 4 capital letters with vertical symmetry.
7. Is a scalene triangle (all sides different) symmetric? Why or why not?

Recap

• A symmetric shape folds along a line into two equal halves.
• A line that makes this fold is a line of symmetry.
• Different shapes have different numbers of symmetry lines.
• A circle has infinite lines of symmetry.