What this chapter is about
Symmetry is all around you. Look at a butterfly, a rangoli, or even your own face in the mirror. When one half of something looks exactly like the other half, we say it has symmetry. This chapter helps you see and understand this beautiful pattern in shapes.
In Class 6, you learn to spot symmetry in flat shapes. You will find out what a line of symmetry is and how to draw it. Some shapes have one such line, some have many, and some have none at all. You will also learn about reflection, which is like seeing an image in a mirror.
After studying this chapter, you should be able to look at any shape and tell whether it is symmetric. You should be able to draw all the lines of symmetry for common shapes. You will also understand how reflection works and how to draw mirror images of simple figures.
Key ideas
- A shape has symmetry when you can fold it along a line and both halves match exactly, like two perfect twins lying on top of each other.
- A line of symmetry is the fold line that divides a shape into two matching halves.
- Some shapes have only one line of symmetry (like the letter A), some have many (like a square has four), and some have none (like the letter R).
- A regular polygon is a shape with all sides equal and all angles equal. A regular polygon with n sides has exactly n lines of symmetry.
- Reflection symmetry means one half is the mirror image of the other half.
- In reflection, every point on one side of the line has a matching point on the other side, at the same distance from the line.
- Nature is full of symmetry: leaves, flowers, insects, and snowflakes often show symmetric patterns.
Formulas and facts to remember
- Line of symmetry: A line that divides a shape into two parts that are mirror images of each other.
- An equilateral triangle (all three sides equal) has exactly 3 lines of symmetry.
- A square has exactly 4 lines of symmetry (two through opposite corners, two through midpoints of opposite sides).
- A rectangle (not a square) has exactly 2 lines of symmetry (through midpoints of opposite sides only).
- A circle has infinitely many lines of symmetry (any line through its centre is a line of symmetry).
- A regular hexagon has 6 lines of symmetry.
- The letters A, H, M, O, T, U, V, W, X, Y (in capital block form) have at least one vertical line of symmetry.
Worked examples
Example 1: Finding lines of symmetry in an isosceles triangle
Rohan draws a triangle with two sides of 5 cm each and one side of 4 cm. How many lines of symmetry does it have?
Step 1: An isosceles triangle has two equal sides. Step 2: If you fold it along a line from the top corner down to the middle of the unequal side, both halves will match. Step 3: There is no other fold that makes the halves match.
Answer: The triangle has 1 line of symmetry.
Example 2: Drawing the reflection of a point
Point P is 3 cm to the left of a vertical line. Where will its reflection be?
Step 1: In reflection, the image is on the opposite side of the line. Step 2: The image is the same distance from the line as the original point. Step 3: So the reflection of P is 3 cm to the right of the line.
Answer: The reflected point is 3 cm to the right of the line.
Example 3: Lines of symmetry in a regular pentagon
A regular pentagon has 5 equal sides. How many lines of symmetry does it have?
Step 1: A regular polygon with n sides has n lines of symmetry. Step 2: Here n = 5.
Answer: A regular pentagon has 5 lines of symmetry.
Common mistakes
Thinking every rectangle has four lines of symmetry → Only a square (a special rectangle) has four; a rectangle that is not a square has only two.
Drawing a line of symmetry that does not divide the shape into matching halves → Always check by imagining a fold; both sides must overlap perfectly.
Believing all triangles have three lines of symmetry → Only an equilateral triangle has three; an isosceles triangle has one, and a scalene triangle has none.
Placing the reflected point at the wrong distance from the line → The reflected point must be at the same distance from the line, just on the opposite side.
Quick revision
- A line of symmetry divides a shape into two matching mirror halves.
- Fold test: if both halves overlap exactly, the fold line is a line of symmetry.
- More equal sides and equal angles usually mean more lines of symmetry.
- A circle has endless lines of symmetry; a scalene triangle has none.
- Reflection places the image at the same distance from the line, on the other side.