What is Symmetry?
A figure has symmetry if one part mirrors the other. Symmetry appears in nature (butterfly wings, flowers), architecture, and everyday objects.
Line symmetry (Bilateral symmetry): A figure can be divided by a line into two identical halves that are mirror images of each other.
- The dividing line is called the line of symmetry or axis of symmetry.
- When folded along the line of symmetry, the two halves overlap perfectly.
Lines of Symmetry in Various Figures
Common Shapes
| Shape | Number of Lines of Symmetry |
|---|---|
| Scalene triangle | 0 |
| Isosceles triangle | 1 |
| Equilateral triangle | 3 |
| Rectangle | 2 (horizontal and vertical) |
| Square | 4 |
| Regular pentagon | 5 |
| Regular hexagon | 6 |
| Circle | Infinite |
| Rhombus | 2 (diagonals) |
| Parallelogram (not rectangle) | 0 |
Rule: A regular polygon with n sides has n lines of symmetry.
Symmetry in Letters of the Alphabet
Capital Letters with Vertical Line of Symmetry (left-right)
A, H, I, M, O, T, U, V, W, X, Y
Capital Letters with Horizontal Line of Symmetry (top-bottom)
B, C, D, E, H, I, K, O, X
Capital Letters with Both (vertical + horizontal)
H, I, O, X
Letters with No Line of Symmetry
F, G, J, L, N, P, Q, R, S, Z
Mirror Reflection (Mirror Image)
When an object is placed in front of a mirror:
- The image appears to be behind the mirror.
- The object and image are equidistant from the mirror.
- The image is laterally inverted — left and right are swapped.
Key Properties
- Left becomes right and right becomes left.
- Top and bottom remain unchanged (for vertical mirror).
- Shape and size are preserved.
Example: Letter "d" in mirror looks like "b". The number 3 in mirror looks like ε (reversed 3).
Drawing Lines of Symmetry
To draw the line of symmetry: 1. Fold the figure mentally (or physically). 2. The fold line where both halves match is the line of symmetry. 3. For shapes on grid paper, use the grid lines as guide.
Figures with Multiple Lines of Symmetry
Some figures have more than one line of symmetry.
Square: 4 lines — 2 through midpoints of opposite sides, 2 through opposite vertices (diagonals).
Regular hexagon: 6 lines — 3 through midpoints of opposite sides, 3 through opposite vertices.
Circle: Every diameter is a line of symmetry → infinite lines.
Symmetry in Nature and Daily Life
| Object | Symmetry |
|---|---|
| Butterfly wings | 1 vertical line |
| Human body (front view) | 1 vertical line |
| Starfish | 5 lines (radial) |
| Snowflake | 6 lines |
| Flower with 4 petals | 4 lines |
Key Vocabulary
| Term | Meaning |
|---|---|
| Symmetry | One part of figure mirrors the other |
| Line of symmetry | The dividing line creating two identical halves |
| Axis of symmetry | Another name for line of symmetry |
| Bilateral symmetry | Symmetry about a single line |
| Lateral inversion | Left-right flip in mirror image |
| Regular polygon | All sides and angles equal |
Exam Tips
- Regular polygon with n sides has n lines of symmetry — key formula.
- Parallelogram: 0 lines of symmetry (not 2 — a common mistake). A rectangle has 2.
- Rhombus: 2 lines of symmetry (along its diagonals), but it's not the same as a square.
- Letters — know which have which type of symmetry (vertical/horizontal/both/none).
- Mirror image: left and right are swapped — top and bottom stay the same (for vertical mirror).
- Circle: infinite lines of symmetry — every diameter is a line of symmetry.