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…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 6 Mathematics — Symmetry. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Symmetry — All 8 Questions Solved
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 order = 4; Rectangle order = 2
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)
Q7. Identify which of the following letters have line symmetry: A, B, C, D, E.
Checking line symmetry for capital letters
Step 1: Letter A - has vertical line of symmetry down the middle - YES
Step 2: Letter B - does NOT have line of symmetry - NO
Step 3: Letter C - does NOT have perfect line symmetry - NO
Step 4: Letter D - does NOT have line of symmetry - NO
Step 5: Letter E - does NOT have line of symmetry - NO
Final Answer: Only letter A has a line of symmetry
Q8. What is the order of rotational symmetry for a rectangle?
Finding the order of rotational symmetry for a rectangle
Step 1: A rectangle has rotational symmetry about its centre
Step 2: When rotated 90°, it does NOT look the same (length and width are different)
Step 3: When rotated 180°, it looks identical
Step 4: When rotated 270°, it does NOT look the same
Step 5: When rotated 360°, it returns to original position
Step 6: Order of rotational symmetry = 2 (at 180° and 360°)
Final Answer: Rectangle has rotational symmetry of order 2
Symmetry — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What does 'symmetry' generally mean in mathematics?
- A. A shape that has many sides.
- B. A shape that looks the same on both sides of a dividing line.
- C. A shape that can be folded only once.
- D. A shape that is very small.
Answer: B. A shape that looks the same on both sides of a dividing line. — Symmetry refers to a shape or object having two sides that are mirror images of each other, usually across a line or a point.
MCQ 2. How many lines of symmetry does a square have?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: D. 4 — A square has four lines of symmetry: two passing through opposite midpoints of sides and two passing through opposite vertices (diagonals).
MCQ 3. Which of these capital letters has only a vertical line of symmetry?
- A. B
- B. C
- C. A
- D. E
Answer: C. A — The letter 'A' has a single vertical line of symmetry that divides it into two mirror halves. Letters B, C, E primarily have horizontal symmetry or no symmetry.
MCQ 4. How many lines of symmetry does an equilateral triangle have?
- A. 1
- B. 2
- C. 3
- D. 0
Answer: C. 3 — An equilateral triangle has three equal sides and three equal angles, resulting in three lines of symmetry, each passing through a vertex and the midpoint of the opposite side.
MCQ 5. How many lines of symmetry does a rectangle have?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: B. 2 — A rectangle has two lines of symmetry: one horizontal line passing through the midpoints of the longer sides and one vertical line passing through the midpoints of the shorter sides.
MCQ 6. Which of the following numbers has a horizontal line of symmetry?
- A. 1
- B. 3
- C. 5
- D. 7
Answer: B. 3 — The number '3' has a horizontal line of symmetry, meaning if you fold it horizontally, both halves match. The numbers 1, 5, 7 do not have a horizontal line of symmetry.
MCQ 7. How many lines of symmetry does an isosceles triangle have?
- A. 0
- B. 1
- C. 2
- D. 3
Answer: B. 1 — An isosceles triangle has two equal sides and two equal base angles, giving it exactly one line of symmetry that passes through the vertex between the equal sides and the midpoint of the base.
MCQ 8. A regular pentagon has how many lines of symmetry?
- A. 3
- B. 4
- C. 5
- D. 6
Answer: C. 5 — A regular polygon with 'n' sides has 'n' lines of symmetry. Since a regular pentagon has 5 sides, it has 5 lines of symmetry.
MCQ 9. Which of these triangles has no line of symmetry?
- A. Equilateral triangle
- B. Isosceles triangle
- C. Scalene triangle
- D. Right-angled isosceles triangle
Answer: C. Scalene triangle — A scalene triangle has all three sides of different lengths and all three angles of different measures, thus it does not have any line of symmetry.
MCQ 10. Which of these everyday objects often shows line symmetry?
- A. A banana
- B. A human hand
- C. A butterfly
- D. A cloud
Answer: C. A butterfly — A butterfly typically has a prominent line of symmetry running down its body, with its wings on either side being mirror images of each other.
MCQ 11. When a square is rotated completely around its centre (360 degrees), how many times does it look exactly the same as its original position?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: D. 4 — A square has a rotational symmetry of order 4. This means it looks the same 4 times during a full 360-degree rotation (at 90, 180, 270, and 360 degrees).
MCQ 12. How many lines of symmetry can a circle have?
- A. 1
- B. 2
- C. 4
- D. Infinite
Answer: D. Infinite — A circle has an infinite number of lines of symmetry, as any line passing through its center will divide it into two identical halves.
MCQ 13. Which of these capital letters has both horizontal and vertical lines of symmetry?
- A. E
- B. X
- C. H
- D. T
Answer: C. H — The letter 'H' has both a horizontal line of symmetry (folding it across its middle) and a vertical line of symmetry (folding it top to bottom).
MCQ 14. Which of these shapes exhibits rotational symmetry (looks the same after turning less than a full circle)?
- A. Scalene triangle
- B. Isosceles trapezoid
- C. Rectangle
- D. Kite
Answer: C. Rectangle — A rectangle has rotational symmetry of order 2, meaning it looks the same after a 180-degree turn. The other shapes generally do not have rotational symmetry.
MCQ 15. A certain letter of the English alphabet has exactly one line of symmetry, which is horizontal. Which letter could it be?
- A. A
- B. B
- C. M
- D. Z
Answer: B. B — The letter 'B' has exactly one line of symmetry, and this line is horizontal. Letters A, M have vertical symmetry, and Z has no line of symmetry.
MCQ 16. A line that divides a figure into two identical halves, such that one half is a mirror image of the other, is called a:
- A. diagonal
- B. axis of rotation
- C. line of symmetry
- D. diameter
Answer: C. line of symmetry — The definition of a line of symmetry is a line that divides a figure into two parts that are exact mirror images of each other.
MCQ 17. Which of the following letters of the English alphabet has no line of symmetry?
- A. A
- B. O
- C. S
- D. M
Answer: C. S — Letters 'A', 'O', and 'M' each have at least one line of symmetry, while the letter 'S' does not have any line that divides it into identical mirror halves.
MCQ 18. A rectangle has how many lines of symmetry?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: B. 2 — A rectangle has two lines of symmetry; these lines join the midpoints of its opposite sides.
MCQ 19. An equilateral triangle has how many lines of symmetry?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: C. 3 — An equilateral triangle has three lines of symmetry, with each line passing through a vertex and the midpoint of the opposite side.
MCQ 20. Which of these shapes has an infinite number of lines of symmetry?
- A. Square
- B. Rectangle
- C. Circle
- D. Equilateral Triangle
Answer: C. Circle — Any line passing through the center of a circle will divide it into two identical halves, and there are infinitely many such lines.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.