Introduction to Symmetry: Class 6 Maths Ex 13.1 (NCERT)

Understanding Symmetry and the Line of Symmetry

Symmetry is when one shape becomes exactly like another if you flip, slide, or turn it. The type of symmetry we are studying in this chapter is called line symmetry or reflectional symmetry. A figure has line symmetry if there is a line that you can draw through it which divides the figure into two identical parts. Think of this line as a mirror. If you place a mirror on this line, the reflection of one half of the figure would perfectly match the other half. This special line is called the line of symmetry or the axis of symmetry. For example, if you take a rectangular sheet of paper and fold it exactly in the middle, the two halves sit perfectly on top of each other. The fold you made is the line of symmetry. Some shapes have one line of symmetry, some have many, and some have none at all!

How to Find the Line of Symmetry

1. Step 1: Observe the Figure — Look closely at the shape or object you want to check for symmetry. You can even trace it onto a piece of paper.
2. Step 2: Imagine Folding — Think about where you could fold the figure so that the two halves match up perfectly. Try imagining folding it vertically (top to bottom), horizontally (left to right), or even diagonally.
3. Step 3: Draw the Line — Once you find a fold that works, draw a dotted line along this fold. This dotted line represents the line of symmetry.
4. Step 4: Verify the Halves — Check if the two parts on either side of the line are exact mirror images of each other. If they are, you have successfully found a line of symmetry. Remember, a shape can have more than one line of symmetry, so repeat the process to find them all.

Examples of Lines of Symmetry in Shapes

• Rectangle: A rectangle has two lines of symmetry. One runs horizontally through the middle, and the other runs vertically through the middle.
• Square: A square has four lines of symmetry. One horizontal, one vertical, and two diagonal lines.
• Equilateral Triangle: A triangle with all sides equal has three lines of symmetry. Each line goes from a corner (vertex) to the midpoint of the opposite side.
• Isosceles Triangle: A triangle with two equal sides has only one line of symmetry. It runs from the vertex between the two equal sides to the midpoint of the base.
• Circle: A circle has infinite lines of symmetry! Any line that passes through its center is a line of symmetry.
• Letter 'A': The capital letter 'A' has one vertical line of symmetry down its middle.
• Letter 'H': The capital letter 'H' has two lines of symmetry: one vertical and one horizontal.

Important Points to Remember

• Not all figures are symmetrical. A shape with no line of symmetry is called an asymmetrical figure. For example, a scalene triangle (all sides different) is asymmetrical.
• The line of symmetry can be vertical, horizontal, or diagonal.
• A line of symmetry is also called a mirror line or axis of symmetry.
• When you complete a figure with a given line of symmetry, the other half must be a perfect mirror image of the given half.

Practice Questions with Solutions

• Q: How many lines of symmetry does an isosceles triangle have? Draw them. A: Step 1: Recall the properties of an isosceles triangle. It has two equal sides and two equal angles. Step 2: Imagine folding the triangle. If you fold it along the line from the vertex between the equal sides to the midpoint of the opposite side, the two halves will match perfectly. Step 3: Try folding it any other way. No other fold will result in matching halves. Final answer: An isosceles triangle has only one line of symmetry.
• Q: The letter 'Z' is given. Is it symmetrical? If yes, find its line of symmetry. A: Step 1: Write down the letter 'Z'. Step 2: Imagine a vertical line through its center. The two halves are not mirror images. Step 3: Imagine a horizontal line through its center. Again, the top and bottom parts are not mirror images. Step 4: Imagine a diagonal line. The parts do not match. Final answer: The letter 'Z' is not symmetrical. It has zero lines of symmetry.
• Q: A shape has a vertical line of symmetry. The left half of the shape looks like the letter 'P'. What does the complete shape look like? A: Step 1: Draw the letter 'P' and a vertical line of symmetry to its right. Step 2: The line of symmetry acts like a mirror. We need to draw the reflection of 'P' on the other side of the line. Step 3: The reflection of 'P' will be a mirror image, a backward 'P'. When you join them, the shape looks like two 'P's back-to-back. Final answer: The complete shape will look like a butterfly or a heart-like shape formed by a 'P' and its mirror image.
• Q: List any three letters of the English alphabet that have a horizontal line of symmetry. A: Step 1: Think of the alphabet letters. A horizontal line of symmetry means the top half is a mirror image of the bottom half. Step 2: Let's check some letters. For 'B', if you draw a horizontal line through the middle, the top curve mirrors the bottom curve. So 'B' works. Step 3: For 'C', a horizontal line through the middle works as well. Step 4: For 'E', a horizontal line through the middle arm creates two matching parts. Final answer: Three letters with a horizontal line of symmetry are B, C, and E. (Others include D, H, I, K, O, X).

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