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

Question 66

What is a line of symmetry?

1. A line of symmetry is an imaginary line that cuts a shape into two exact mirror halves.
2. If you fold the shape on that line, both parts match perfectly.
3. We will check two simple lines:
   • Vertical line (up–down)
   • Horizontal line (left–right)
4. Important: We are using standard block letters. In fancy fonts the answer can change.

Step-by-step check (letter by letter)

S

• Try a vertical line: the top and bottom curves do not match. ❌
• Try a horizontal line: the left and right parts do not match. ❌
• So, S has 0 lines of symmetry.

Y

• Try a vertical line down the middle: left and right halves match.
• Try a horizontal line: top and bottom do not match. ❌
• So, Y has 1 line of symmetry (vertical).

M

• Try a vertical line down the middle: left and right halves match.
• Try a horizontal line: top and bottom do not match. ❌
• So, M has 1 line of symmetry (vertical).

E

• Try a vertical line: the open side would flip to the other side, so it changes. ❌
• Try a horizontal line through the middle: top bar and bottom bar swap places; the letter looks the same.
• So, E has 1 line of symmetry (horizontal).

T

• Try a vertical line down the center: left and right halves match.
• Try a horizontal line: the stem would point the other way, so it changes. ❌
• So, T has 1 line of symmetry (vertical).

R

• Try a vertical line: the curved and slanted parts don’t match. ❌
• Try a horizontal line: top and bottom don’t match. ❌
• So, R has 0 lines of symmetry.

Y (again at the end)

• Same as before: 1 line (vertical).

Final Answer (letter → number of symmetry lines)

Therefore: S–0, Y–1, M–1, M–1, E–1, T–1, R–0, Y–1.

Note: These counts are for standard block-style capital letters. In stylized fonts, symmetry can be different.