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

Question 2

1. Understand “line of symmetry”.
   A line of symmetry is a line that splits a shape into two exact mirror halves.
   If you fold the shape on this line, both halves match perfectly.

2. Recall what a scalene triangle is.
   In a scalene triangle, all three sides are different in length.
   Write it as: (a eq b), (b eq c), and (c eq a).

3. Try to find a possible symmetry line.
   Suppose a symmetry line exists. Then the two parts on either side of that line must be identical.

4. Case 1: Line passes through a vertex.
   If the line goes through a vertex and splits the opposite side into two equal parts, then the two sides meeting at that vertex must be equal for the halves to match.
   That would give ( ext{side}_1 = ext{side}_2 ) (like an isosceles triangle).
   But a scalene triangle has ( ext{side}_1 eq ext{side}_2 ).
   Contradiction.

5. Case 2: Line passes through the midpoint of a side.
   For mirror halves, the angles touching that side must also match.
   That would force two angles to be equal: ( angle A = angle B ) (for example).
   Equal angles usually imply two equal opposite sides, which again goes against (a eq b eq c).
   Contradiction.

6. Conclusion.
   Every possible “mirror line” forces some sides or angles to become equal, but a scalene triangle has no equal sides or angles.
   Therefore, a scalene triangle has no line of symmetry.

Answer: 0

Quick option check

• 0 Correct for a scalene triangle.
• 1 ❌ This happens for an isosceles triangle.
• 2 ❌ Not possible for triangles.
• 3 ❌ This happens for an equilateral triangle.