Symmetry: CBSE Class 6 Maths

Understanding Symmetry and the Line of Symmetry

In simple words, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip, or slide. For our lesson, we are focusing on line symmetry. A figure has line symmetry if a line can be drawn dividing the figure into two identical parts that are mirror images of each other. This dividing line is called the line of symmetry or the axis of symmetry.

Imagine you have a paper cutout of a heart. If you can fold it exactly in half so that the two halves match up perfectly, then the fold line is the line of symmetry. When you unfold it, the shape is balanced on both sides of the fold. Some shapes have one line of symmetry, some have many, and some have none at all! This concept helps us understand the properties of geometric shapes much better.

How to Find a Line of Symmetry

1. The Folding Method — This is the most intuitive way. Take a cutout of the shape. Try folding it along a line. If one half of the figure falls exactly on top of the other half, the fold line is a line of symmetry. You can try folding it in different ways (vertically, horizontally, diagonally) to find all possible lines of symmetry.
2. The Mirror Method — Place a small mirror on the shape along a line. If the reflection of one part of the shape in the mirror looks exactly like the other part of the shape, then that line is a line of symmetry. This is why line symmetry is also called reflectional symmetry.

Lines of Symmetry in Common Geometric Shapes

• Square: A square has 4 lines of symmetry. Two lines join the midpoints of opposite sides, and two lines are the diagonals.
• Rectangle: A rectangle has 2 lines of symmetry. These are the lines joining the midpoints of its opposite sides. (Note: The diagonals are NOT lines of symmetry).
• Equilateral Triangle: A triangle with all sides equal has 3 lines of symmetry. Each line goes from a vertex to the midpoint of the opposite side.
• Isosceles Triangle: A triangle with two equal sides has only 1 line of symmetry. This line bisects the angle between the two equal sides and goes to the midpoint of the third side.
• Circle: A circle has infinite lines of symmetry. Any line passing through the center of the circle is a line of symmetry.
• Scalene Triangle: A triangle with no equal sides has 0 lines of symmetry.

Important Tips & Common Mistakes

Many students make a common mistake with rectangles and parallelograms. Remember:

• A Rectangle's Diagonal is NOT a line of symmetry. If you fold a rectangular paper along its diagonal, the corners will not match up perfectly. A rectangle has only two lines of symmetry, which are horizontal and vertical.
• A Parallelogram generally has NO lines of symmetry. Unless it's a special type like a rectangle or a rhombus, a standard parallelogram cannot be folded perfectly in half.
• Count carefully! Always double-check if you have found all the lines of symmetry for a shape. For regular polygons (like an equilateral triangle, square, regular pentagon), the number of lines of symmetry is equal to the number of sides.

Practice Questions with Solutions

• Q: How many lines of symmetry does the letter 'X' have? Draw them.
  A: Step 1: Think of the letter 'X' as two intersecting lines. Let's try folding it.
  Step 2: If we draw a horizontal line through the center, the top part is a mirror image of the bottom part. This is one line of symmetry.
  Step 3: If we draw a vertical line through the center, the left part is a mirror image of the right part. This is the second line of symmetry.
  Final answer: The letter 'X' has 2 lines of symmetry.

• Q: A triangle has only one line of symmetry. What type of triangle is it?
  A: Step 1: Let's recall the properties of different triangles. A scalene triangle has no equal sides and no lines of symmetry.
  Step 2: An equilateral triangle has all three sides equal and has 3 lines of symmetry.
  Step 3: An isosceles triangle has two equal sides. The line that runs from the vertex between the equal sides to the midpoint of the opposite side is a line of symmetry. It only has this one line.
  Final answer: The triangle is an isosceles triangle.

• Q: Complete the following figure so that the dotted line is the line of symmetry.
  (Imagine a drawing of the letter 'L' with a vertical dotted line to its right.)
  A: Step 1: The dotted line is the mirror line. We need to draw the reflection of the given shape on the other side of the line.
  Step 2: Every point on the new side must be at the same distance from the mirror line as its corresponding point on the original side, but in the opposite direction.
  Step 3: Drawing the reflection of the 'L' shape will create a shape that looks like the letter 'U'.
  Final answer: The completed figure will look like the letter 'U'.

• Q: How many lines of symmetry does a regular hexagon have?
  A: Step 1: A regular hexagon is a polygon with 6 equal sides and 6 equal angles.
  Step 2: There are lines of symmetry that join opposite vertices. Since there are 6 vertices, there are 3 pairs of opposite vertices. This gives us 3 lines of symmetry.
  Step 3: There are also lines of symmetry that join the midpoints of opposite sides. Since there are 6 sides, there are 3 pairs of opposite sides. This gives us another 3 lines of symmetry.
  Step 4: Total lines of symmetry = 3 (through vertices) + 3 (through midpoints of sides) = 6.
  Final answer: A regular hexagon has 6 lines of symmetry.

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