Symmetry Class 6 Notes | Chapter 13 Maths

What is Symmetry?

Symmetry is a core concept in geometry that describes a sense of balanced and harmonious proportion. An object or shape is said to be symmetrical if it can be divided into two identical halves that are mirror images of each other. Think of a butterfly's wings or your own face; there's a line down the middle, and the left side looks like a reflection of the right side. This imaginary dividing line is called the line of symmetry or axis of symmetry. If you were to fold a symmetrical shape along its line of symmetry, the two parts would match up perfectly. This property is also known as reflectional symmetry. In contrast, a figure that cannot be divided into two identical halves is called an asymmetrical or non-symmetrical figure. Understanding symmetry is not just for maths class; it helps us appreciate patterns in nature (like in leaves and flowers), design (logos and buildings), and art.

Key Terms in Symmetry

Symmetry

A property where a figure or object can be divided by a line into two parts that are exact mirror images of each other.

Line of Symmetry

The imaginary line that divides a figure into two identical, mirror-image halves. It is also called the axis of symmetry.

Symmetrical Figure

A figure that has at least one line of symmetry.

Asymmetrical Figure

A figure that has no lines of symmetry.

Reflection

The 'flipping' of a point or shape over a line (the line of symmetry). The reflected image is the same size and shape as the original.

Mirror Image

The reflected duplicate of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface.

Multiple Lines of Symmetry

A property of some figures that have more than one line of symmetry. For example, a square has four lines of symmetry.

Must Remember

• {"point":"A line of symmetry can be vertical, horizontal, or diagonal."}
• {"point":"An equilateral triangle has 3 lines of symmetry."}
• {"point":"An isosceles triangle has only 1 line of symmetry."}
• {"point":"A scalene triangle has 0 lines of symmetry."}
• {"point":"A rectangle has 2 lines of symmetry (bisecting the sides), but its diagonals are not lines of symmetry."}
• {"point":"A square has 4 lines of symmetry (two bisecting the sides and two diagonals)."}
• {"point":"A circle has infinite lines of symmetry, as any line passing through its center is a line of symmetry."}
• {"point":"Some English alphabet letters like A, H, M, O, T, U, V, W, X, Y have lines of symmetry."}

How to Find the Line of Symmetry

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Examples: Lines of Symmetry in Shapes and Alphabets

• Isosceles Triangle An isosceles triangle has 2 equal sides. The line of symmetry runs from the vertex between the equal sides to the midpoint of the opposite base. It has 1 line of symmetry.
• Letter 'H' The letter 'H' can be folded perfectly in half both vertically and horizontally. Therefore, it has 2 lines of symmetry.
• Letter 'S' No matter how you try to fold the letter 'S', the two halves will not match up. It has 0 lines of symmetry. (Note: It has rotational symmetry, which you will learn in higher classes).

Common Exam Mistake

A very common error is confusing the diagonals of a rectangle and a parallelogram as lines of symmetry. They are not! If you fold a rectangle along its diagonal, the corners will not match up. A rectangle only has two lines of symmetry (the lines joining the midpoints of opposite sides). A square has four, including its diagonals. Always visualize the fold or draw it to be sure.

Quick Revision Check

• How many lines of symmetry does a regular pentagon have? A regular pentagon has 5 lines of symmetry.
• Name two letters of the English alphabet that have no lines of symmetry. F, G, J, L, N, P, Q, R, S, Z.
• Does a kite have a line of symmetry? If yes, how many? Yes, a kite has one line of symmetry along its main diagonal (the one that connects the vertices between equal sides).
• What is the difference in the number of lines of symmetry between a square and a rhombus? A square has 4 lines of symmetry, while a rhombus has 2 (its diagonals).

Frequently Asked Questions about Symmetry

Frequently Asked Questions