NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and SolutionsQuestion 66
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions
Question. 66
Write the number of lines of symmetry in each letter of the word ‘SYMMETRY’.
Answer:
S–0, Y–1, M–1, M–1, E–1, T–1, R–0, Y–1
Detailed Answer with Explanation:
Q66. Lines of Symmetry in the word SYMMETRY
Goal: For each capital letter, tell how many lines of symmetry it has.
What is a line of symmetry?
- A line of symmetry is an imaginary line that cuts a shape into two exact mirror halves.
- If you fold the shape on that line, both parts match perfectly.
- We will check two simple lines:
- Vertical line (up–down)
- Horizontal line (left–right)
- 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)
| Letter | Lines of Symmetry | Direction (if any) |
|---|---|---|
| S | 0 | — |
| Y | 1 | Vertical |
| M | 1 | Vertical |
| M | 1 | Vertical |
| E | 1 | Horizontal |
| T | 1 | Vertical |
| R | 0 | — |
| Y | 1 | Vertical |
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.