Q33. Letters with both horizontal and vertical lines of symmetry
Goal: Find how many capital letters in English have both a vertical line of symmetry (left ↔ right) and a horizontal line of symmetry (top ↔ bottom).
Step 1: Understand “line of symmetry”
- Vertical line of symmetry: If you draw a straight line from top to bottom through the middle, the left side and right side look exactly the same.
- Horizontal line of symmetry: If you draw a straight line from left to right through the middle, the top part and bottom part look exactly the same.
- A letter we want must pass both tests.
Step 2: Use a simple “fold test”
Imagine folding the letter along a line:
- If both halves match perfectly after folding top over bottom, it has horizontal symmetry.
- If both halves match perfectly after folding left over right, it has vertical symmetry.
Step 3: Check the letters that commonly work
Try these four carefully. They are drawn in standard block (print) style.
-
H
- Vertical symmetry: Left bar and right bar are mirror images across the middle line.
- Horizontal symmetry: Top part and bottom part match across the middle bar.
-
I
- Vertical symmetry: Left and right sides of the vertical stroke match.
- Horizontal symmetry: Top and bottom look the same around the center.
-
O
- Vertical symmetry: A circle/oval looks the same on both sides of a vertical middle line.
- Horizontal symmetry: A circle/oval looks the same on both sides of a horizontal middle line.
-
X
- Vertical symmetry: The left slant and right slant reflect across a vertical middle line.
- Horizontal symmetry: The upper slant and lower slant reflect across a horizontal middle line.
Step 4: Why other letters don’t qualify
- Some letters (like A, M, T, U, V, W, Y) may have vertical symmetry, but they do not have horizontal symmetry in standard block style.
- Others (like B, C, D, E, F, …) fail at least one of the two tests.
Final Answer
There are 4 letters: H, I, O, X.