Learning Objectives
- Understand the concept of symmetry and lines of symmetry
- Identify symmetrical figures and draw lines of symmetry
- Recognise symmetry in everyday objects, letters, and shapes
- Understand reflection symmetry
Key Concepts
What Is Symmetry?
A figure has symmetry if one half of it is a mirror image of the other half. If you fold a symmetrical figure along a special line, both halves match exactly. This special line is called the line of symmetry or the axis of symmetry. Symmetry makes shapes look balanced and beautiful.
Line of Symmetry
A line of symmetry divides a figure into two identical halves that are mirror images of each other. Some figures have one line of symmetry (e.g., the letter A), some have more than one (e.g., a rectangle has 2, an equilateral triangle has 3), and some have no line of symmetry at all (e.g., the letter R).
Symmetry in Regular Shapes
A circle has infinite (unlimited) lines of symmetry — every diameter is a line of symmetry.
A square has 4 lines of symmetry (2 diagonals + 2 lines through midpoints of opposite sides).
An equilateral triangle has 3 lines of symmetry.
A rectangle has 2 lines of symmetry (through midpoints of opposite sides).
A regular polygon with n sides has n lines of symmetry.
Symmetry in Letters and Objects
English capital letters with vertical line of symmetry: A, H, I, M, O, T, U, V, W, X, Y. Letters with horizontal line of symmetry: B, C, D, E, H, I, K, O, X. Letters with both: H, I, O, X. Many objects around us show symmetry: butterflies, leaves, faces, buildings, and rangoli patterns.
Reflection Symmetry
When you look in a mirror, you see your reflection. The mirror acts as the line of symmetry. This is called reflection symmetry. The reflected image is the same size and shape as the original but appears flipped. The image and the object are at equal distances from the mirror line.
Summary
Symmetry is an important concept found in nature, art, and mathematics. A figure is symmetrical if it can be divided into two identical halves by a line of symmetry. Different shapes have different numbers of lines of symmetry. A circle has unlimited lines, while some shapes have none. Reflection symmetry is seen when an object and its mirror image are identical.
Important Terms
- Symmetry: An exact match or balance on either side of a dividing line
- Line of Symmetry: A line that divides a figure into two identical mirror-image halves
- Reflection: The mirror image of a shape across a line of symmetry
- Symmetrical Figure: A figure that has at least one line of symmetry
- Asymmetrical Figure: A figure that has no line of symmetry
Quick Revision
- A circle has infinite lines of symmetry; a square has 4; an equilateral triangle has 3
- A rectangle has 2 lines of symmetry (NOT along the diagonals)
- A parallelogram has no line of symmetry
- A regular polygon with n sides has n lines of symmetry
- The mirror image is at the same distance from the line of symmetry as the original
- Symmetry is found in nature: butterfly wings, flower petals, human faces
- Fold test: if you fold a shape along a line and both halves match, that line is a line of symmetry