NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - True or False Questions
Question 56

Question. 56

A circle has only 16 lines of symmetry.

Answer:

false

Detailed Answer with Explanation:

Idea:

( ext{A line of symmetry} ) is a line that splits a shape into two exact matching halves.

  1. Think about a circle.

    ( ext{Every line that passes through the centre of the circle} )

    ( ext{cuts it into two equal halves.} )

  2. You can draw many such lines:

    ( ext{1 line, 2 lines, 10 lines, 16 lines, 100 lines, ...} )

    There is no last one—you can always draw another line through the centre.

  3. So the number of symmetry lines for a circle is

    ( ext{not limited to 16.} )

    ( ext{It is infinite.} )

Why the statement is false:

( ext{"Only 16"} Rightarrow ext{wrong, because we can draw more than 16.} )

( ext{In fact, infinitely many lines of symmetry exist for a circle.} )

Quick check:

( ext{Try drawing lines (diameters) through the centre at different angles.} )

( ext{Each one makes two matching halves. There is no limit.} )

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