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Symmetry

NCERT Class 5 · Mathematics Based on NCERT Class 5 Mathematics textbook · Free CBSE study kit

Chapter Notes

**Reflection Symmetry (Folding):**

  • Line of symmetry = fold line where shape mirrors itself
  • Vertical line of symmetry = left and right halves are mirror images
  • Horizontal line of symmetry = top and bottom halves are mirror images
  • Diagonal line of symmetry = corner to corner mirror image
  • **Rotational Symmetry (Spinning):**

  • Shape looks identical after rotating less than full turn
  • 1/4 turn = 90° rotation
  • 1/2 turn = 180° rotation
  • 3/4 turn = 270° rotation
  • Full turn = 360° rotation
  • **Key Facts:**

  • Letter A: 1 vertical line of symmetry
  • Letter H: 2 lines of symmetry (vertical + horizontal) + rotational at 1/2 turn
  • Firki: Rotational symmetry at every 1/4 turn
  • Some shapes have only reflection, some only rotational, some have both
  • **Diagrams to Remember:** Fold marks, rotation arrows with quarter divisions, mirror lines

    **Don't Confuse:** Reflection = folding (mirror image). Rotational = spinning (same appearance after turn).

    MCQs — 10 Questions with Answers

    Q1. Which alphabet letter has a vertical line of symmetry?

    • A. Letter E
    • B. Letter N
    • C. Letter A ✓
    • D. Letter K

    Answer: C — Letter A has a vertical line of symmetry running down the middle, making the left and right halves mirror images.

    Q2. How many quarter turns make one full turn?

    • A. 2 quarter turns
    • B. 3 quarter turns
    • C. 4 quarter turns ✓
    • D. 5 quarter turns

    Answer: C — One full turn equals 4 quarter turns because each quarter turn is 1/4 of 360 degrees.

    Q3. Which of the following has rotational symmetry at 1/4 turn?

    • A. A firki (windmill) ✓
    • B. A triangle
    • C. The letter C
    • D. A rectangle

    Answer: A — A firki has rotational symmetry because it looks identical after spinning by 1/4, 1/2, and 3/4 turns.

    Q4. To make a paper cutout of letter H by folding, how many times should you fold the paper?

    • A. Fold once
    • B. Fold twice (to make quarters) ✓
    • C. Fold three times
    • D. Do not fold

    Answer: B — Letter H has two lines of symmetry, so you fold once vertically and once horizontally to make quarters, then draw 1/4 of the letter.

    Q5. Which statement about reflection symmetry is correct?

    • A. Reflection symmetry means spinning a shape
    • B. Reflection symmetry means folding a shape so one half mirrors the other ✓
    • C. Reflection symmetry only works with triangles
    • D. Reflection symmetry needs a dot in the center

    Answer: B — Reflection symmetry is when you fold a shape along a line and both halves look like mirror images of each other.

    Q6. In the firki activity, after which turns does the firki look the same? (Fill in the blanks) The firki looks the same after _____, _____, _____, and a full turn.

    • A. 1/4, 1/2, 3/4 ✓
    • B. 1/3, 2/3, 1
    • C. 1/2, 3/4, 1
    • D. 1/8, 1/4, 1/2

    Answer: A — A firki has 4-fold rotational symmetry, so it looks identical after 1/4 turn, 1/2 turn, 3/4 turn, and a full turn.

    Q7. Which digit has both reflection symmetry AND rotational symmetry?

    • A. Digit 5
    • B. Digit 8 ✓
    • C. Digit 2
    • D. Digit 3

    Answer: B — The digit 8 has a horizontal line of symmetry (reflection) and looks the same when rotated 1/2 turn (rotational symmetry).

    Q8. Which of the following is an example of block printing with rotational symmetry?

    • A. A print that looks the same after 1/4 turn ✓
    • B. A print that is the same when folded
    • C. A print with only one line of symmetry
    • D. A print with no symmetry

    Answer: A — Block printing designs with rotational symmetry repeat identically when the pattern is rotated by 1/4, 1/2, or 3/4 turns.

    Q9. How many lines of symmetry does the letter O have?

    • A. 1 line
    • B. 2 lines
    • C. 4 lines
    • D. Infinite lines ✓

    Answer: D — A circle (letter O) has infinite lines of symmetry because any line through its center creates a mirror image.

    Q10. When you fold a square paper diagonally twice and cut along the X pattern for a firki, what do you create?

    • A. A shape with only reflection symmetry
    • B. A shape with only rotational symmetry
    • C. A firki that spins with rotational symmetry ✓
    • D. A shape with no symmetry

    Answer: C — The firki activity creates a spinning toy with 4-fold rotational symmetry that looks identical every 1/4 turn.

    Flashcards

    What is reflection symmetry?

    When a shape can be folded along a line so one half is an exact mirror image of the other half.

    What is a line of symmetry?

    The fold line where a shape looks the same on both sides as if reflected in a mirror.

    How many lines of symmetry does letter A have?

    Letter A has 1 vertical line of symmetry down the middle.

    How many lines of symmetry does letter H have?

    Letter H has 2 lines of symmetry: 1 vertical down the middle and 1 horizontal across the middle.

    What is rotational symmetry?

    When a shape looks the same after being rotated (spun) around its centre point by less than a full turn.

    If a shape has rotational symmetry at 1/4 turn, what does this mean?

    The shape looks identical when rotated by 1/4 of a full turn (90 degrees).

    What is the relationship between quarter turn and half turn?

    A half turn equals 2 quarter turns, and a full turn equals 4 quarter turns.

    Which alphabet letter has both reflection and rotational symmetry?

    Letter H has both reflection symmetry (vertical and horizontal lines) and rotational symmetry (at 1/2 turn).

    How do you make an alphabet cutout using reflection symmetry?

    Fold paper in half, draw half the letter along the fold, cut, then open to see the full letter.

    What does a firki (windmill) demonstrate?

    A firki demonstrates rotational symmetry because it looks the same after every 1/4 turn.

    Important Board Questions

    What is reflection symmetry? Give one example from the chapter. [1 mark]

    Define reflection as folding so halves are mirror images; give any letter example like A, H, or O.

    Draw a vertical line of symmetry on the letter H and explain why H has two lines of symmetry. [2 marks]

    Draw letter H with a vertical line down the middle and a horizontal line across the middle; explain each makes a mirror image.

    Explain how you would make a paper cutout of letter A using the folding method. What would you do in each step? [3 marks]

    Four steps: fold paper in half, draw half the letter A on the fold, cut along outline, open the paper. Explain why folding works (uses reflection symmetry).

    A firki (windmill) has rotational symmetry. Describe what happens when you rotate the firki by 1/4 turn, 1/2 turn, 3/4 turn, and a full turn. Does it look the same each time? Explain why a firki has rotational symmetry. [5 marks]

    Describe that firki looks identical at each rotation point due to its 4-fold symmetrical design; explain rotational symmetry means shape appears unchanged after spinning less than full turn.

    True or False: A shape can have both reflection symmetry and rotational symmetry. Give one example from the chapter to support your answer. [2 marks]

    Answer is True; give letter H as example (has reflection symmetry with vertical and horizontal lines, and rotational symmetry at 1/2 turn) OR digit 8.

    Next chapterPerimeter and Area →

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