Chapter 10 · NCERT Class 5 Maths Mela

Symmetrical Designs

Look at a butterfly, a rangoli, or the letter A. Each has two halves that match like a mirror image. That matching is called symmetry, and the fold line is the line of symmetry. Tap each idea and start spotting symmetry everywhere!

🦋 3 topics⏱ ~20 min📝 10-question quiz

Play with it

Six ideas about symmetry

Symmetry is all about matching halves. Tap each word to see what it means, with a design you can picture.

Explore · Symmetrytap a word

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The three big ideas

A line of symmetry divides a shape into two halves that match exactly when you fold along it.
It works like a mirror: one half is the reflection of the other, so it is also called the mirror line.
Easy test: trace the shape, fold along a line, and see if the two halves sit perfectly on top of each other.

Worked example. You cut out a paper butterfly and fold it straight down the middle. The left wing lands exactly on the right wing. Does it have a line of symmetry?

The two halves match perfectly when folded, so yes — the middle fold is a line of symmetry.

A shape can have more than one line of symmetry. A square has 4, a rectangle has 2.
A circle has very many — any line through its centre folds it into matching halves.
The letter A has just 1 (down the middle), and a letter like F has none.

Common mix-up: a rectangle's diagonals are NOT lines of symmetry — fold along a diagonal and the corners do not match. Only a square's diagonals work.

Many rangoli and kolam patterns are built around lines of symmetry — that is what makes them look so balanced.
Nature is full of symmetry too: a leaf, a flower, a butterfly's wings.
You can make your own symmetrical design: draw half a pattern, then fold and copy it onto the other side.

Where you'll meet it

Symmetry around you

Festival rangoli & kolam

At Diwali, Pongal and Onam, families draw rangoli and kolam at the doorstep. Folding the design in your mind shows the matching halves — symmetry is the secret to their balance.

Symmetry in nature

A peacock's open feathers, a tulsi leaf, a lotus, a butterfly — look closely and you can imagine the mirror line that splits each into two matching halves.

Folded-paper art

Fold a paper, snip a few bits, and open it — you get a symmetrical design every time. The fold becomes the line of symmetry.