- Drawing and craft
- Classes 3-5
- 4 min read
Symmetry and rangoli patterns
Discover lines of symmetry in shapes, letters and rangoli, and learn to draw a pattern whose two halves match.
Let us begin
The big idea
Look at a butterfly. Its left wing and right wing match like a mirror. This is called symmetry. Rangoli artists use symmetry to make beautiful patterns for festivals.
A shape is symmetrical when you can draw a line through it so that both halves match exactly, like a mirror. This line is called a line of symmetry or mirror line.
If you fold the shape along its line of symmetry, the two halves fit exactly on top of each other.
Some shapes have more than one line of symmetry. A square has 4. A rectangle that is not a square has 2. An equilateral triangle (all sides equal) has 3. A circle has many, because every line through its centre works.
Rangoli is a floor pattern made at festivals and celebrations. In Tamil Nadu it is called kolam and in West Bengal it is called alpana. Many rangoli and kolam patterns are symmetrical, so they are drawn on a grid of dots with the same design on both sides.
To copy a point to the other side of a mirror line, keep the same height and the same distance from the line, but on the opposite side.
Worked examples
See how it works
Lines of symmetry of a square
A square has 4 lines of symmetry: 1 line joining the middle points of the top and bottom sides, 1 line joining the middle points of the left and right sides, and 2 diagonals. So the answer is 4.
Letters
The letter A has 1 vertical line of symmetry. The letter H has 2 lines: one up and down, and one across. The letter F has no line of symmetry.
Finishing a pattern
On the left of the mirror line there is a dot 3 cm away from the line and 2 cm above the bottom. On the right side, draw a dot 3 cm away from the line, also 2 cm above the bottom. Now the two sides match.
Try it at home
Draw my own rangoli
You will need
- A sheet of paper
- A pencil and a ruler
- Crayons or colour pencils
What to do
- Draw a dotted grid of 5 rows and 5 dots in each row, with equal gaps.
- Draw a dashed vertical line down the middle dot column. This is your mirror line.
- On the left side only, join some dots with straight lines or curves to make a pattern.
- Copy the same pattern on the right side, like a mirror.
- Colour both halves with the same colours in the same places.
Ask a grown-up: An adult can help you rule the dashed line and check that both halves match.
Practice sheet
Check what you learned
Practice sheet: Symmetry and rangoli patterns (Classes 3-5, Drawing and craft)
- What is a line of symmetry?
- How many lines of symmetry does a square have?
- How many lines of symmetry does a rectangle (that is not a square) have?
- How many lines of symmetry does an equilateral triangle have?
- How many lines of symmetry does the capital letter A have?
- How many lines of symmetry does a circle have?
- How many lines of symmetry does the capital letter H have?
- Does the capital letter F have a line of symmetry?
- The left half of a pattern has a flower at the top left. Where will the matching flower be on the right half?
- Name one thing in nature that shows symmetry.
Answer key
Answers: Symmetry and rangoli patterns
- A line that cuts a shape into two halves that match exactly, like a mirror.
- 4.
- 2.
- 3.
- 1 (a vertical line).
- Many. Every line through the centre is a line of symmetry.
- 2 (one up and down, one across).
- No.
- At the top right, at the same distance from the mirror line.
- Sample answers: a butterfly, a leaf, a flower or a face.