Symmetry
Many shapes in nature and design look balanced because they are symmetric. This Class 6 Ganita Prakash chapter explains line symmetry, where a figure matches its mirror image across a line, shows how to find lines of symmetry in shapes and letters, and introduces rotational symmetry.
Learning objectives
- Understand line (reflection) symmetry.
- Find the lines of symmetry of a figure.
- Recognise symmetry in letters and everyday shapes.
- Identify simple rotational symmetry.
Key concepts
Line symmetry
A figure has line symmetry if a line can divide it into two halves that are mirror images of each other. That line is called the line of symmetry or axis of symmetry — folding the figure along it makes the two halves match exactly.
Lines of symmetry in shapes
Different shapes have different numbers of lines of symmetry. A rectangle has 2, an equilateral triangle has 3, and a square has 4, while a circle has countless lines of symmetry through its centre. Some shapes, like a scalene triangle, have none.
Symmetry in letters and objects
Capital letters show symmetry too: A, M and T have a vertical line of symmetry, B and E have a horizontal one, and H and X have both. Many natural and made objects — butterflies, leaves, flags and rangoli designs — are built on the same idea of balance.
Rotational symmetry
A figure has rotational symmetry if it looks the same after being turned by less than a full turn about its centre. A square looks the same after a quarter turn, so it has rotational symmetry, while the number of matching positions in one full turn is its order of rotational symmetry.
Key definitions
- Line of symmetry
- A line that divides a figure into two mirror-image halves.
- Reflection symmetry
- Another name for line symmetry, based on a mirror image.
- Rotational symmetry
- When a figure looks the same after a turn of less than 360°.
- Axis of symmetry
- The line along which a symmetric figure can be folded to match.
Solved examples
Q1. How many lines of symmetry does a square have?
Solution: Four — two diagonals and the two lines joining midpoints of opposite sides.
Q2. Does the letter H have a line of symmetry?
Solution: Yes, it has both a vertical and a horizontal line of symmetry.
Q3. How many lines of symmetry does a scalene triangle have?
Solution: None, because no line divides it into mirror-image halves.
Common mistakes to avoid
- Assuming every shape has at least one line of symmetry.
- Thinking a rectangle has 4 lines of symmetry (it has only 2).
- Confusing line symmetry with rotational symmetry.
- Drawing a line of symmetry that does not give matching halves.
Symmetry — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
A line that divides a figure into two mirror-image halves is a:
Practice questions
Short answer
What is a line of symmetry?
A line that divides a figure into two mirror-image halves.
How many lines of symmetry does a square have?
Four.
Give a letter with only a vertical line of symmetry.
A (or M, or T).
Long answer
Explain line symmetry and give the number of lines of symmetry for a rectangle, an equilateral triangle and a circle.
A figure has line symmetry when a straight line, called the line of symmetry, divides it into two halves that are exact mirror images — folding along the line makes the halves match. Different shapes have different numbers of such lines: a rectangle has 2 (the lines joining midpoints of opposite sides), an equilateral triangle has 3 (one from each vertex), and a circle has countless lines of symmetry, since any line through its centre divides it into matching halves.
What is the difference between line symmetry and rotational symmetry? Illustrate with a square.
Line symmetry is about reflection: a line divides the figure into mirror-image halves. Rotational symmetry is about turning: the figure looks the same after a rotation of less than a full turn about its centre. A square shows both — it has 4 lines of symmetry (so 4-fold line symmetry), and it also has rotational symmetry because it looks identical after each quarter turn (90°), matching itself 4 times in a full turn. So a shape can have one kind of symmetry, both, or neither.
HOTS (Higher Order Thinking)
Which capital letters have a horizontal line of symmetry but not a vertical one?
Letters such as B, C, D and E have a horizontal line of symmetry but no vertical one.
A shape looks the same after every quarter turn. How many times does it match itself in one full turn?
Four times, since a full turn (360°) contains four quarter turns.
Quick revision
Revision notes
- Line symmetry: a line splits a figure into mirror-image halves.
- Lines of symmetry — rectangle 2, equilateral triangle 3, square 4, circle countless.
- Letters: A/M/T vertical; B/E horizontal; H/X both.
- Rotational symmetry: looks the same after a turn less than 360°.
Key takeaways
- Symmetry is about balance — by reflection or by turning.
- Not every shape has a line of symmetry.
- A figure can have line symmetry, rotational symmetry, or both.
Frequently asked questions
What is line symmetry?
A figure has it when a line divides it into two mirror-image halves.
How many lines of symmetry does an equilateral triangle have?
Three.
What is rotational symmetry?
When a figure looks the same after being turned by less than a full turn about its centre.