Chapter 10 · ICSE Class 5 Math

Symmetry

A shape is symmetric if you can fold it so both halves match exactly. Tap a shape and see its line(s) of symmetry appear as dashed lines.

The Symmetry Machine
4 lines of symmetry

Try it: tap the letter F — some shapes have no lines of symmetry at all.

10.1

What is symmetry?

A shape has symmetry if it can be divided by a line — called the line of symmetry — into two halves that are exact mirror images of each other. If you folded the shape along that line, both halves would match perfectly.

Everyday example — A butterfly's wings are symmetric — the left and right sides mirror each other around the body. Try tapping the Square in the Symmetry Machine above to see all 4 of its lines of symmetry.
10.2

Lines of symmetry in shapes

Square
4 lines
Rectangle
2 lines
Equilateral Triangle
3 lines
10.3

Symmetry in letters

1One line of symmetry

Letters like A, M, and T have exactly one line of symmetry — a vertical line down the middle.

2No lines of symmetry

Letters like F, G, and P have no line of symmetry at all — no fold makes the two sides match.

3Two lines of symmetry

The letter H has two lines of symmetry — one vertical and one horizontal.

10.4

Worked examples

1Counting lines of symmetry

How many lines of symmetry does a regular pentagon (5 equal sides) have?

A regular shape has as many lines of symmetry as it has sides: 5 lines

2A circle

How many lines of symmetry does a circle have?

Infinite — any line through the centre is a line of symmetry

Watch out — Not every shape with two equal-looking halves is symmetric. The line has to create an exact mirror image — a shape can look balanced overall but still have zero true lines of symmetry, like the letter S.
Practice

Exercises

Tap a question to reveal its answer once you've tried it yourself.

Assess

Sample tests

Two 20-mark, 30-minute tests. Reveal answers question by question.