The letter Z exhibits a rotational symmetry of order 2.
Understanding Rotational Symmetry
Rotational symmetry describes how a shape or object appears identical to its original form after being rotated by a specific angle around a central point. The "order" of rotational symmetry indicates the number of times the shape perfectly aligns with its initial appearance within a complete 360-degree rotation, excluding the 0-degree (original) position.
For the letter Z, an order of 2 signifies that it achieves congruence with its starting orientation twice during a full circle rotation. Specifically, if you rotate the letter Z by 180 degrees around its geometric center, it will look exactly the same as it did before the rotation. A further 180-degree turn (for a total of 360 degrees) would bring it back to its absolute initial state.
Symmetry Properties of the Letter Z
While the letter Z clearly demonstrates rotational symmetry, it is important to note that it does not possess line symmetry (also known as reflectional symmetry). Line symmetry requires a line to be drawn through the shape, dividing it into two perfectly mirrored halves. The letter Z does not have any such line.
The symmetry characteristics of the letter Z, alongside other common English alphabets, are presented in the following table, sourced from Vedantu.com:
| Alphabets | Line Symmetry | Order of Rotational Symmetry |
|---|---|---|
| Z | No | 2 |
| S | No | 2 |
| H | Yes | 2 |
| O | Yes | 2 |
Reference: Some English alphabets have fascinating symmetrical structures...
This specific type of rotational symmetry, where the order is 2, is often referred to as point symmetry.
