Write three capital letters of the English alphabet which have both rotational symmetry and reflection symmetry.
The correct answer and explanation is:
Correct Answer: H, I, O
Explanation:
In the English alphabet, some capital letters show specific types of symmetry. There are two main types of symmetry to consider:
- Reflection symmetry (mirror symmetry): A letter has reflection symmetry if it can be divided into two equal halves that are mirror images. This can be vertical, horizontal, or both.
- Rotational symmetry: A letter has rotational symmetry if it looks the same after being rotated 180 degrees (a half turn).
To qualify for both reflection and rotational symmetry, a letter must remain unchanged when rotated 180 degrees and must also have a mirror image along at least one axis.
Letter H has both vertical and horizontal reflection symmetry. If split down the middle vertically or across the middle horizontally, the halves match. Additionally, when rotated 180 degrees, it looks the same.
Letter I has both vertical and horizontal reflection symmetry, depending on its font. It also has rotational symmetry because it appears the same when flipped upside down.
Letter O is a perfect example of both types of symmetry. It has infinite lines of reflection symmetry and looks identical when rotated by 180 degrees.
These three letters meet the criteria because:
- They remain unchanged when turned halfway around (rotational symmetry).
- They can be split evenly into mirrored halves (reflection symmetry).
Letters like X or N may appear symmetrical at first glance, but X has reflection symmetry but no proper rotational symmetry unless turned 90 degrees, which is not the standard for defining 180-degree rotational symmetry in this context. N fails rotational symmetry because it becomes a backward N when rotated.
Therefore, H, I, and O are the correct capital letters that have both reflection symmetry and rotational symmetry.