Introduction to 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 introduction, we will focus on line symmetry. A figure has line symmetry if a line can be drawn dividing the figure into two identical parts. 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 fold it exactly in the middle from top to bottom, the left half will perfectly cover the right half. The fold line you made is the heart's line of symmetry. The two halves are mirror images of each other. Some shapes, like a rectangle, have two lines of symmetry (one horizontal and one vertical). A square is even more special; it has four lines of symmetry! However, some figures, like a scalene triangle (where all sides are different lengths), have no lines of symmetry at all.

A Step-by-Step Guide to Finding the Line of Symmetry

1. Step 1: Observe the Figure — Look at the shape carefully. Think about its properties. Does it have equal sides or equal angles? This can give you a clue about where a line of symmetry might be.
2. Step 2: Perform the 'Fold Test' — Imagine folding the shape along a straight line. You can try folding it horizontally, vertically, or even diagonally.
3. Step 3: Check for Perfect Overlap — After folding, does one half of the figure completely and exactly cover the other half? There should be no parts sticking out. If they match perfectly, you've found a line of symmetry.
4. Step 4: Identify All Possible Lines — Don't stop after finding one line! Some shapes have more. Try folding the shape in other ways to see if other lines of symmetry exist. For example, a square has four lines of symmetry.

Lines of Symmetry in Different Shapes

• Isosceles Triangle: Has 1 line of symmetry. This line runs from the vertex between the two equal sides to the middle of the opposite base.
• Rectangle: Has 2 lines of symmetry. One line connects the midpoints of the longer sides, and the other connects the midpoints of the shorter sides.
• Square: Has 4 lines of symmetry. Two lines connect the midpoints of opposite sides, and two lines are the diagonals.
• Equilateral Triangle: Has 3 lines of symmetry. Each line runs from a vertex to the midpoint of the opposite side.
• Circle: Has infinite lines of symmetry. Any line that passes through the center of the circle is a line of symmetry.
• Scalene Triangle: Has 0 lines of symmetry because none of its sides or angles are equal, so it cannot be folded to create two matching halves.

Important Points About Symmetry

• The line of symmetry is also called the 'axis of symmetry' or the 'mirror line'.
• A figure may have no line of symmetry, one line of symmetry, or multiple lines of symmetry.
• The two halves of a symmetrical figure are congruent, meaning they have the exact same size and shape.
• A diagonal is not always a line of symmetry. For a rectangle, the diagonals are not lines of symmetry, but for a square, they are.

Practice Questions with Solutions

• Q: How many lines of symmetry does the letter 'H' have? A: Step 1: Visualize the letter 'H'. Imagine folding it. Step 2: If we fold it horizontally across the middle bar, the top half perfectly covers the bottom half. This is one line of symmetry. Step 3: If we fold it vertically down the middle, the left half perfectly covers the right half. This is a second line of symmetry. Final answer: The letter 'H' has 2 lines of symmetry.
• Q: A figure has a vertical line of symmetry. The left half of the figure is drawn. How would you complete the figure? A: Step 1: Treat the line of symmetry as a mirror. Step 2: For every point on the left half of the figure, imagine its reflection on the right side, at the same distance from the mirror line. Step 3: Connect these reflected points on the right side to create a mirror image of the left side. Final answer: The completed figure will be a whole, symmetrical shape where the right side is a perfect mirror image of the given left side.
• Q: A regular pentagon has 5 equal sides and 5 equal angles. How many lines of symmetry does it have? A: Step 1: A regular polygon is a shape with all sides and all angles equal. Step 2: In any regular polygon, the number of lines of symmetry is equal to the number of sides. Step 3: A regular pentagon has 5 sides. Final answer: A regular pentagon has 5 lines of symmetry. Each line passes through a vertex and the midpoint of the opposite side.
• Q: Is the dotted line shown in a picture of a parallelogram a line of symmetry? A: Step 1: A parallelogram has opposite sides that are equal and parallel. The dotted line shown is one of its diagonals. Step 2: Imagine folding the parallelogram along this diagonal. Step 3: The two triangles formed by the diagonal are congruent, but when you fold them, they do not overlap perfectly. The vertices will not match up. Final answer: No, the diagonal of a parallelogram is not a line of symmetry.

Frequently Asked Questions