NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Multiple Choice Questions
Question 3

Question.  3

The number of lines of symmetry in a circle is

(A)

0

(B)

2

(C)

4

(D)

more than 4

Detailed Answer with Explanation:

  1. Understand the term:

    A line of symmetry is a line that splits a shape into two mirror-image halves.

  2. Think about a circle:

    A circle looks the same from every direction. It has no corners and every point on the circle is the same distance from the center.

  3. Use the center to find symmetry lines:

    Draw a straight line through the center of the circle. This straight line is a diameter.

    Each diameter divides the circle into two equal halves that match exactly.

  4. Try many diameters:

    Draw one diameter — you get 1 line of symmetry.

    Rotate a little and draw another diameter — now you have 2 lines of symmetry.

    Keep rotating and drawing new diameters through the center — you can make as many as you want.

  5. Key idea:

    Because you can rotate by any small angle and still draw a new diameter, the number of symmetry lines is not limited.

    Mathematically, we say the circle has infinitely many lines of symmetry.

    In symbols: the count is ( ext{infinite}).

  6. Match with the options:

    It is not 0, not 2, and not 4. It is more than 4 (actually infinitely many).

Final Answer: Option D — “more than 4.”

Why the other options are incorrect
  • 0: A circle clearly has symmetry (any diameter works), so not 0.
  • 2: You can draw more than two diameters through the center.
  • 4: You are not limited to just four; you can draw many more.
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