Symmetry (Reflection & Rotation) Quiz - ICSE Class 8 Mathematics

Free practice quiz: Symmetry (Reflection & Rotation) (ICSE Class 8 Mathematics). 53 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 53 multiple-choice questions on Symmetry (Reflection & Rotation), and 53 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. A square has how many lines of symmetry passing through its center?

   1. 1
   2. 2
   3. 3
   4. 4
   Show answer

   Answer: D. 4

   A square has four lines of symmetry. Two lines pass through opposite vertices, and two lines pass through the midpoints of opposite sides. All these lines intersect at the center.

2. Which of the following letters of the English alphabet has no symmetry?

   1. A
   2. M
   3. P
   4. R
   Show answer

   Answer: D. R

   The letter A has reflectional symmetry. The letter M has reflectional symmetry. The letter P has reflectional symmetry. The letter R has neither reflectional nor rotational symmetry (of order > 1).

3. The point of intersection of the diagonals of a square is the center for which types of symmetry?

   1. Only reflectional symmetry
   2. Only rotational symmetry
   3. Both reflectional and rotational symmetry
   4. Neither reflectional nor rotational symmetry
   Show answer

   Answer: C. Both reflectional and rotational symmetry

   The diagonals of a square intersect at its center. This center is a point of rotational symmetry of order 4. Additionally, the lines containing the diagonals are lines of reflectional symmetry. Therefore, the intersection point is the center for both types of symmetry.

4. If a figure has rotational symmetry of order 4, it will coincide with its original position after rotations of which of the following angles?

   1. 72 degrees
   2. 90 degrees
   3. 120 degrees
   4. 150 degrees
   Show answer

   Answer: B. 90 degrees

   Rotational symmetry of order 4 means the figure coincides with its original position every 360/4 = 90 degrees. So, it coincides at 90, 180, 270, and 360 degrees.

5. Which of the following figures has no rotational symmetry other than a full 360-degree rotation?

   1. Square
   2. Equilateral Triangle
   3. Scalene Triangle
   4. Circle
   Show answer

   Answer: C. Scalene Triangle

   A square has rotational symmetry of order 4. An equilateral triangle has rotational symmetry of order 3. A circle has infinite rotational symmetry. A scalene triangle has no rotational symmetry of order greater than 1 (only the trivial 360-degree rotation).

More questions in this quiz

Answers and explanations are in the full quiz.

1. Which of the following letters of the English alphabet has rotational symmetry of order 2?
2. A regular hexagon has how many lines of symmetry?
3. What is the order of rotational symmetry of an equilateral triangle?
4. Which of the following shapes has only one line of symmetry?
5. If a shape has rotational symmetry of order 4, how many times does it appear in the same position when rotated through 360 degrees?
6. Which of the following letters has both reflectional and rotational symmetry?
7. What is the minimum angle of rotation about its center that a regular pentagon needs to appear in its original position?
8. Which of the following shapes has rotational symmetry of order 3?
9. A kite has how many lines of symmetry?
10. The shape of a badminton racquet is most like which of the following symmetries?
11. If a figure has reflectional symmetry across a horizontal line and a vertical line, what kind of rotational symmetry must it also possess?
12. What is the order of rotational symmetry for a rectangle?
13. Which of the following angles of rotation would map a regular octagon onto itself?
14. A shape has exactly three lines of symmetry. What is the minimum number of sides it must have?
15. Which of the following letters has reflectional symmetry across a horizontal line but NOT across a vertical line?
16. What is the order of rotational symmetry of a parallelogram that is not a rhombus or a rectangle?
17. Consider a right-angled isosceles triangle. How many lines of symmetry does it possess?
18. If a shape has rotational symmetry of order 3, what is the smallest angle of rotation that maps it onto itself?
19. Which of the following shapes has reflectional symmetry but not rotational symmetry of order greater than 1?
20. How many lines of symmetry does a rhombus have?
21. Which of the following letters possesses rotational symmetry of order 2?
22. If a shape has rotational symmetry of order 4, what is its angle of rotational symmetry?
23. Which of the following shapes does NOT have reflectional symmetry?
24. Consider the letter 'W'. What type of symmetry does it possess?
25. If a shape has rotational symmetry of order 3, it also has an angle of rotational symmetry of:
26. Which of the following statements is true about a regular pentagon?
27. What is the minimum number of lines of symmetry a polygon can have to also possess rotational symmetry of order greater than 1?
28. Which letter has point symmetry but no line symmetry?
29. A scalene triangle has:
30. What is the minimum number of sides a polygon must have to exhibit rotational symmetry of order 3?
31. Which of the following shapes has exactly two lines of symmetry?
32. If a figure has rotational symmetry of order 2 and reflectional symmetry across two perpendicular lines, what is the minimum order of rotational symmetry it can have?
33. Which of the following statements about symmetry is FALSE?
34. What is the angle of rotation for rotational symmetry of order 5?
35. Which of the following letters has only reflectional symmetry across a vertical line?
36. The graph of the function y = x^2 is symmetric about which axis?
37. If a figure has exactly one line of symmetry, it can have:
38. What is the minimum number of sides a polygon must have to have both reflectional and rotational symmetry?
39. If a letter has horizontal symmetry and vertical symmetry, it must also have:
40. Which of the following letters has reflectional symmetry across a diagonal line?
41. What is the number of lines of symmetry for a regular dodecagon (12-sided polygon)?
42. Which of the following has rotational symmetry of order 1 only?
43. The shape of a snowflake is often characterized by which type of symmetry?
44. A figure is symmetric with respect to the origin. This means it has:
45. Which of the following has no lines of symmetry and no rotational symmetry of order greater than 1?
46. The number of lines of symmetry in a regular n-sided polygon is:
47. Which shape has rotational symmetry of order 3 AND reflectional symmetry?
48. Consider a regular pentagon. What is its order of rotational symmetry?

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