Symmetry — Class 6 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Symmetry" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Symmetry" — 8 important questions with detailed answers for CBSE board exam prepara…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

What is a line of symmetry? Give an example.
How many lines of symmetry does a rectangle have?
Draw a line of symmetry for a circle.
What is rotational symmetry? Explain with an example.
How many lines of symmetry does an equilateral triangle have?
Does an isosceles triangle have a line of symmetry?
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
What is a line of symmetry? Give an example.	✓ Solved
How many lines of symmetry does a rectangle have?	✓ Solved
Draw a line of symmetry for a circle.	✓ Solved
What is rotational symmetry? Explain with an example.	✓ Solved
How many lines of symmetry does an equilateral triangle h…	✓ Solved
Does an isosceles triangle have a line of symmetry?	✓ Solved

Showing 6 of 8 questions

Q1: What is a line of symmetry? Give an example.

A line of symmetry is a line that divides a shape into two mirror-image halves Step 1: If you fold the shape along this line, both halves match exactly Step 2: Example: A square has 4 lines of symmetry Step 3: Two diagonal lines and two lines through the midpoints of opposite sides Step 4: When folded along any of these, the two halves coincide perfectly Final Answer: A line of symmetry divides a shape into identical mirror halves. Square example has 4 such lines

Q2: How many lines of symmetry does a rectangle have?

Identifying lines of symmetry in a rectangle Step 1: A rectangle has two axes of symmetry Step 2: One vertical line through the midpoints of the top and bottom sides Step 3: One horizontal line through the midpoints of the left and right sides Step 4: If you fold along these lines, the halves match exactly Step 5: Diagonal lines do NOT fold to match in a rectangle Final Answer: A rectangle has 2 lines of symmetry

Q3: Draw a line of symmetry for a circle.

Identifying lines of symmetry for a circle Step 1: A circle is perfectly symmetric Step 2: Any line passing through the centre of the circle is a line of symmetry Step 3: You can fold the circle along any diameter Step 4: Both halves match exactly Step 5: Since there are infinitely many diameters, a circle has infinite lines of symmetry Final Answer: Any line through the centre of a circle is a line of symmetry (infinite lines)

Q4: What is rotational symmetry? Explain with an example.

Rotational symmetry is when a shape looks the same after rotation about a fixed point Step 1: The fixed point is called the centre of rotation Step 2: The angle of rotation is how much the shape turns Step 3: Example: A square has rotational symmetry of order 4 Step 4: When rotated 90°, 180°, 270°, and 360° about its centre, it looks the same Step 5: A rectangle has rotational symmetry of order 2 (at 180° rotation) Final Answer: Rotational symmetry: shape looks identical after rotation. Square o...

Q5: How many lines of symmetry does an equilateral triangle have?

Identifying lines of symmetry in an equilateral triangle Step 1: An equilateral triangle has all sides equal and all angles equal (60° each) Step 2: Line 1: From vertex to midpoint of opposite side Step 3: Line 2: From second vertex to midpoint of its opposite side Step 4: Line 3: From third vertex to midpoint of its opposite side Step 5: Each line divides the triangle into two congruent halves Final Answer: An equilateral triangle has 3 lines of symmetry

Q6: Does an isosceles triangle have a line of symmetry?

Identifying line of symmetry in an isosceles triangle Step 1: An isosceles triangle has two equal sides Step 2: The line of symmetry passes through the vertex angle (where equal sides meet) Step 3: This line goes from the vertex to the midpoint of the base Step 4: When folded along this line, the two equal sides match exactly Step 5: The two base angles also match Final Answer: Yes, an isosceles triangle has 1 line of symmetry (through vertex and base midpoint)

Showing 6 of 8 questions. Visit the full page for complete solutions.