NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions
Question 55

Question. 55

A square and a rectangle have the same number of lines of symmetry.

Answer:

false

Detailed Answer with Explanation:

Let’s understand step by step.

  1. Meaning first: A line of symmetry is a line that splits a shape into two equal mirror halves.
  2. For a square:
    • Fold through the middle up–down (vertical). That works.
    • Fold through the middle left–right (horizontal). That works.
    • Fold along the first diagonal. That works.
    • Fold along the second diagonal. That works.

    Total for a square:

    (4)

  3. For a rectangle (not a square):
    • Vertical middle line works.
    • Horizontal middle line works.
    • Diagonals do not work because sides are not all equal.

    Total for a rectangle:

    (2)

  4. Compare:

    5. ( ext{Square} = 4 quad ext{and}quad ext{Rectangle} = 2 )

    ( 4 e 2 )

Conclusion: The statement is false because a square has 4 lines of symmetry, while a rectangle has only 2.

Quick check tip: Try folding a paper square and a paper rectangle to see which folds match perfectly.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 9: Symmetry and Practical Geometry – True or False Questions | Detailed Answers