Mastery

Symmetry — Mastery

30 questions 30 min Full-chapter mastery

Q1. An isosceles triangle (two equal sides) has lines of symmetry equal to
- A. 1
- B. 2
- C. 3
- D. 0
Q2. A regular pentagon has lines of symmetry equal to
- A. 5
- B. 4
- C. 3
- D. 10
Q3. The paper windmill has the smallest angle of rotational symmetry equal to
- A. 45 deg
- B. 60 deg
- C. 180 deg
- D. 90 deg
Q4. A figure that returns to itself only after a 180 deg rotation and a 360 deg rotation has order of rotational symmetry equal to
- A. 2
- B. 1
- C. 3
- D. 4
Q5. A figure with 6 equal radial arms equally spaced about its centre has the smallest angle of symmetry equal to
- A. 30 deg
- B. 60 deg
- C. 90 deg
- D. 120 deg
Q6. In the ink-blot devils activity, a paper is folded once, ink is spilled on one half, and the halves are pressed together. The shape obtained on opening is symmetric because
- A. The ink dries before opening the paper
- B. Both halves carry equal weight of ink
- C. The paper is rectangular
- D. The ink on one half stamps a mirror image on the other half along the fold
Q7. Which of the following figures from the chapter has NEITHER a line of symmetry NOR rotational symmetry (smallest angle less than 360 deg)?
- A. Cloud
- B. Rangoli
- C. Flower
- D. Wheel
Q8. A Class 6 teacher wants to introduce the idea of a line of symmetry to her students for the first time. Which of these is the BEST first activity?
- A. Showing a slide of the Taj Mahal and asking students to point to symmetry
- B. Asking students to fold a paper rectangle in half and check if the two halves overlap
- C. Giving the formal definition first and then drawing labelled diagrams
- D. Asking students to compute the perimeter of various polygons
Q9. A square ABCD has A (top-left), B (top-right), C (bottom-right), D (bottom-left). On reflection along the horizontal line of symmetry, the points A and B respectively go to positions earlier occupied by
- A. B and A respectively
- B. C and D respectively
- C. D and C respectively
- D. Themselves
Q10. A figure has 90 deg as its smallest angle of symmetry. Which of the following angles is NOT an angle of symmetry of this figure?
- A. 180 deg
- B. 270 deg
- C. 360 deg
- D. 45 deg
Q11. A regular six-petal flower (like the yellow flower image) has lines of symmetry equal to
- A. 1
- B. 3
- C. 5
- D. 6
Q12. Following the regular polygon sequence starting from triangle, the numbers of lines of symmetry are
- A. 1, 2, 3, 4, 5, ...
- B. 2, 3, 4, 5, 6, ...
- C. 3, 4, 5, 6, 7, ...
- D. 3, 6, 9, 12, 15, ...
Q13. Why is it said that the circle does NOT have a smallest angle of symmetry?
- A. Because a circle has no straight edges
- B. Because every positive angle, however small, is an angle of symmetry — there is no smallest one
- C. Because a circle has only 360 deg as its angle of symmetry
- D. Because the circle is not really a geometric figure
Q14. A square paper is folded once along its vertical midline and then once along its horizontal midline. A simple cut is made through all four layers along the corner of the folded paper. On unfolding, how many lines of symmetry does the resulting hole pattern have?
- A. 1
- B. 2
- C. 3
- D. 4
Q15. A Class 6 student says, 'Any figure with rotational symmetry must also have a line of symmetry.' Which is the BEST way for the teacher to address this misconception?
- A. Tell the student the statement is wrong and move on
- B. Show the paper windmill and ask the student to find any fold that produces matching halves
- C. Show a circle as a counter-example only
- D. Ask the student to write the definition five times in the notebook
Q16. A kite-shaped quadrilateral (two pairs of equal adjacent sides) has lines of symmetry equal to
- A. Exactly 1
- B. Exactly 2
- C. Exactly 4
- D. 0
Q17. An arrow-shaped pentagon (with a pointed tip and a flat tail, lying horizontally) has a line of symmetry that is
- A. Horizontal, passing through the tip and the middle of the tail
- B. Vertical, passing through the tip
- C. Both horizontal and vertical
- D. There is no line of symmetry
Q18. To create a small square hole exactly at the centre of a square paper using folds and a single straight cut, a student should
- A. Cut a small square at one corner without folding
- B. Cut along a diagonal of the unfolded paper
- C. Fold the paper diagonally once and cut a triangle from the tip
- D. Fold the paper in half twice (vertical then horizontal) and cut a small square at the closed corner
Q19. A figure that has one or more lines of symmetry is also said to have
- A. Translational symmetry
- B. Spherical symmetry
- C. Numerical symmetry
- D. Reflection symmetry
Q20. Consider these statements: I. A butterfly has line symmetry but no rotational symmetry. II. The Ashoka Chakra has both line symmetry and rotational symmetry. III. A cloud has rotational symmetry but no line symmetry. Which is/are correct?
- A. I and II only
- B. II and III only
- C. I and III only
- D. II only
Q21. Of the following everyday objects, which one has rotational symmetry of an infinite number of angles?
- A. A bicycle wheel rim (a perfect circle ignoring spokes)
- B. A regular three-blade ceiling fan
- C. A square table top
- D. A regular five-pointed star
Q22. Assertion (A): The capital letter M (when drawn symmetrically) has a vertical line of symmetry. Reason (R): The two slanted strokes of M are mirror images of each other across the centre. Choose the correct option.
- A. Both A and R are true, and R is the correct explanation of A.
- B. Both A and R are true, but R is NOT the correct explanation of A.
- C. A is true, R is false.
- D. A is false, R is true.
Q23. In the chapter, a vertical fold is represented by
- A. A sheet folded so the right half goes behind the left half, with an arrow showing the right going to the left
- B. A sheet folded so the top half goes behind the bottom half
- C. A circle with a diameter drawn through it
- D. A square cut into two horizontal strips
Q24. Folding a figure along its line of symmetry shows that
- A. The part on one side is the reflection of the part on the other side
- B. The line of symmetry is also the diameter of the figure
- C. The figure has rotational symmetry of order 4
- D. The two parts are coloured differently
Q25. The 'three-arm radial human figure' (Q3(d)) has order of rotational symmetry equal to
- A. 2
- B. 4
- C. 6
- D. 3
Q26. Of the following options, which is the BEST way for a teacher to test whether students have understood the '360-factor' rule for the smallest angle of symmetry?
- A. Ask students to memorise the factors of 360
- B. Ask students to draw a regular hexagon
- C. Ask students to write the definition of rotational symmetry in their notebook
- D. Ask students to decide which of 30 deg, 45 deg, 40 deg and 17 deg can be a smallest angle of symmetry, with reasoning
Q27. A rotation of 270 deg is also called a
- A. Half turn
- B. Quarter turn
- C. Full turn
- D. Three-quarter turn
Q28. A Class 6 teacher uses the punching-game activity to teach lines of symmetry. The BEST sequence to maximise learning is
- A. Punch, then state the rule, then ask students to copy
- B. State the rule, punch, then move on
- C. Ask students to predict where holes will appear after unfolding, then punch and observe, then discuss the result
- D. Skip the activity and use only a textbook diagram
Q29. The kolam image has 6-fold structure built around a central hexagon. Its lines of symmetry are best described as
- A. Only 1 vertical line of symmetry
- B. Only 2 perpendicular lines of symmetry
- C. Only 3 lines through opposite corners
- D. 6 lines — through opposite corners and through midpoints of opposite sides of the central hexagon
Q30. Consider the following statements about the pinwheel image (firki / paper windmill) shown at the start of the chapter: I. It has 4 lines of symmetry. II. It has rotational symmetry about its centre. III. The smallest angle of rotational symmetry for it is 90 deg. Which is/are correct?
- A. I and II only
- B. I and III only
- C. All three
- D. II and III only

Your score and per-question explanations appear here instantly.