NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions
Question 64

Question. 64

Write all the capital letters of the English alphabets which have more than one lines of symmetry.

Answer:

H, I, O, X

Detailed Answer with Explanation:

64. Write all the capital letters of the English alphabets which have more than one lines of symmetry.

Answer

H, I, O, X

Explanation — very beginner friendly

Step 1: Understand the idea.

  • A line of symmetry is a line that splits a shape into two matching halves.
  • If you fold a shape on that line, the two parts overlap exactly.
  • Vertical line of symmetry: a straight line from top to bottom (like |).
  • Horizontal line of symmetry: a straight line from left to right (like ).
  • Some letters may also have diagonal symmetry (slanting lines).

Step 2: We need letters with more than one line of symmetry.

Let’s test the letters one by one (think of simple block-style capital letters):

  • H
    • Fold along a vertical line through the middle ⟶ left and right match.
    • Fold along a horizontal line through the middle ⟶ top and bottom match.
    • So, H has 2 lines of symmetry (vertical and horizontal).
  • I (block “I”, not with fancy serifs)
    • Fold along the vertical middle line ⟶ halves match.
    • Fold along the horizontal middle line ⟶ halves match.
    • So, I has 2 lines of symmetry (vertical and horizontal).
  • O (think of a perfect oval/circle shape)
    • Fold along the vertical middle line ⟶ halves match.
    • Fold along the horizontal middle line ⟶ halves match.
    • In a perfect circle there are many symmetry lines, but for the letter shape we count at least these two.
    • So, O has more than one line of symmetry.
  • X
    • Fold along the diagonal from top-left to bottom-right ⟶ halves match.
    • Fold along the diagonal from top-right to bottom-left ⟶ halves match.
    • (Vertical or horizontal folds usually don’t match for X.)
    • So, X has 2 lines of symmetry (the two diagonals).

Step 3: Final list.

The capital letters with more than one line of symmetry are: H, I, O, X.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 9: Symmetry and Practical Geometry – Problems and Solutions | Detailed Answers