NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions

Question 46

Why the statement is false

1. First, recall the meanings:

   ( ext{Isosceles triangle: two sides equal})

   ( ext{Equilateral triangle: three sides equal})

   ( ext{Line of symmetry: a fold/line that makes the two halves match})

2. What we know about symmetry:

   ( ext{Any isosceles triangle has exactly one line of symmetry})

   ( ext{(the line through its vertex and the midpoint of the base).})

   ( ext{Any equilateral triangle has three lines of symmetry})

   ( ext{(one through each vertex and midpoint of the opposite side).})

3. Now suppose an isosceles triangle had more than one line of symmetry.

   ( ext{More than one} ;Rightarrow; ext{at least two symmetry lines})

4. What does a second symmetry line force?

   ( ext{A second symmetry line swaps a different pair of sides})

   (Rightarrow; ext{that pair must also be equal})

   ( ext{So all three sides become equal})

   (Rightarrow; ext{the triangle is equilateral})

5. Therefore:

   ( ext{If a triangle has more than one symmetry line,})

   (Rightarrow; ext{it must be equilateral.})

   ( ext{So the given statement is false.})