NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Multiple Choice Questions

Question 13

Explanation (Very Beginner Friendly)

Correct Option: A (0)

Key Idea

A line of symmetry is a line that splits a shape into two exact mirror halves. If you fold the shape along this line, both parts match perfectly.

Understand the Object

• A compass (used for drawing circles) has two legs.
• One leg holds a pencil.
• The other leg has a metal point (needle).
• So, the two sides are not the same.

Step-by-Step Check for Symmetry

1. Try a vertical line through the middle.
   Left side (pencil) ≠ Right side (needle). They don’t match.
   ⇒ No vertical line of symmetry.
2. Try a horizontal line through the middle.
   Top part ≠ Bottom part (shape and parts are different).
   ⇒ No horizontal line of symmetry.
3. Try a slanted line (any angle).
   Because the legs and their ends (pencil vs needle) are different, folding along any slanted line also won’t match.
   ⇒ No slanted line of symmetry.

Why Options B, C, D are Wrong

• 1 line (B): would need both sides to be the same across that line — they are not.
• 2 lines (C): needs even more sameness — not possible here.
• 3 lines (D): only very regular shapes (like an equilateral triangle has 3) have this — a compass is not one.

Conclusion

Since the two legs are dissimilar (pencil vs needle), the compass has no line of symmetry.

Common Mistake

Do not confuse the compass with a V-shape having equal sides. Even if the angle looks similar, the ends are different, so it is not symmetric.