Introduction to Symmetry Ex 13.2 Class 6 Maths NCERT

What is Symmetry?

Symmetry is a concept where a shape or object looks exactly the same when it is flipped, turned, or cut in a specific way. Think of it like looking into a mirror! If you can draw a line through a figure such that one side is a perfect mirror image of the other side, then that figure has line symmetry. This imaginary line is called the line of symmetry.

For example, if you fold a piece of paper exactly in half and then cut out a heart shape along the fold, when you open it, both halves of the heart will be identical. The fold line is the line of symmetry. Some figures might have only one line of symmetry, like an isosceles triangle, while others, like a square, can have many. Understanding line symmetry helps us classify shapes and appreciate the balanced designs in nature and man-made objects.

Key Terms for Symmetry

Symmetry

A property of an object or shape where one part is a mirror image of the other, or when it looks the same after a transformation (like flipping or turning).

Line of Symmetry (Axis of Symmetry)

An imaginary line that divides a figure into two identical halves, such that if the figure is folded along this line, the two halves perfectly match.

Symmetric Figure

A figure that possesses at least one line of symmetry, meaning it can be divided into two identical mirror-image parts.

Asymmetric Figure

A figure that does not have any line of symmetry, meaning it cannot be divided into two identical mirror-image parts by any straight line.

How to Find and Draw Lines of Symmetry

1. Step 1: Understand the Figure — Look at the given shape carefully. Is it a polygon (like a square, rectangle, triangle) or a curved figure (like a circle)? Imagine folding it.
2. Step 2: Identify Potential Fold Lines — Mentally (or with a ruler on paper), try drawing lines through the center of the figure. Ask yourself: 'If I fold the figure along this line, will both sides match perfectly?'
3. Step 3: Test Horizontal and Vertical Lines — Start by trying a horizontal line through the middle. Then try a vertical line through the middle. For a rectangle, both of these would be lines of symmetry. For an isosceles triangle, only the vertical line from the apex to the base will work.
4. Step 4: Test Diagonal Lines (for squares/rhombuses) — For figures like squares or rhombuses, don't forget to check diagonal lines. A square has two diagonal lines of symmetry in addition to its horizontal and vertical ones. A rectangle, however, does not have diagonal lines of symmetry.
5. Step 5: Count and Draw All Lines — Once you confirm a line creates a perfect mirror image, draw it clearly. Continue until you are sure you have found all possible lines of symmetry for that specific figure. A circle has infinitely many lines of symmetry, as any line passing through its center is a line of symmetry.

Exam Tip: Avoiding Common Mistakes in Symmetry

Students often make a few common errors when dealing with lines of symmetry. One frequent mistake is assuming that all regular polygons have diagonal lines of symmetry. While squares and rhombuses do, a rectangle does not. Remember, a line of symmetry means a perfect mirror image upon folding. If one half hangs over the other, it's not a line of symmetry. Another error is missing lines, especially for shapes like squares or equilateral triangles, which have multiple lines. Always systematically check horizontal, vertical, and diagonal possibilities. For letters of the alphabet, make sure you consider the exact font style, as printed letters might differ slightly from handwritten ones.

Practice Questions with Solutions

• Q: Draw the lines of symmetry for a square.
• A: Step 1: Draw a square. Step 2: Draw a horizontal line through the middle. This is one line of symmetry. Step 3: Draw a vertical line through the middle. This is a second line of symmetry. Step 4: Draw a diagonal line from one corner to the opposite corner. This is a third line of symmetry. Step 5: Draw another diagonal line from the other two opposite corners. This is a fourth line of symmetry. Final answer: A square has 4 lines of symmetry.
• Q: How many lines of symmetry does an isosceles triangle have?
• A: Step 1: Recall an isosceles triangle has two sides of equal length. Step 2: Draw an isosceles triangle. Step 3: Imagine a line from the vertex between the two equal sides, down to the midpoint of the opposite base. If you fold along this line, the two sides will perfectly match. Step 4: Try drawing any other horizontal, vertical (not from the top vertex), or diagonal lines. None of these will divide the triangle into two identical halves. Final answer: An isosceles triangle has 1 line of symmetry.
• Q: Which of the following letters has a horizontal line of symmetry: A, B, C, F?
• A: Step 1: Consider letter A. If you draw a horizontal line through it, the top half is different from the bottom half. No. Step 2: Consider letter B. If you draw a horizontal line through its middle, the top half is a mirror image of the bottom half. Yes. Step 3: Consider letter C. If you draw a horizontal line through its middle, the top curve mirrors the bottom curve. Yes. Step 4: Consider letter F. If you draw a horizontal line through it, the top half is different from the bottom half. No. Final answer: Letters B and C have a horizontal line of symmetry.
• Q: Draw a figure that has no line of symmetry (an asymmetric figure).
• A: Step 1: Think of a simple irregular shape. Step 2: An example could be a scalene triangle (all sides of different lengths). Step 3: Draw a scalene triangle. Try to draw any line through it; you will find that no line can divide it into two identical, mirror-image halves. Final answer: A scalene triangle is one example of a figure with no line of symmetry.

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