Rotational Symmetry — Solutions

1. Order of Rotational Symmetry — Shapes

   1. Order 3, minimum angle 120° ▶ View Solution
   2. Order 4, minimum angle 90° ▶ View Solution
   3. Order 2, minimum angle 180° ▶ View Solution
   4. Order 6, minimum angle 60° ▶ View Solution
   5. Order 2, minimum angle 180° ▶ View Solution
   6. Order 2, minimum angle 180° ▶ View Solution
   7. Order 1 (no rotational symmetry) ▶ View Solution
   8. Infinite order ▶ View Solution

2. True or False

   1. True ▶ View Solution
   2. True ▶ View Solution
   3. False — a parallelogram has 0 lines of symmetry ▶ View Solution
   4. True ▶ View Solution
   5. True ▶ View Solution
   6. True ▶ View Solution
   7. True — every shape maps to itself after a full 360° turn ▶ View Solution
   8. True ▶ View Solution

3. Find the Minimum Angle

   1. 180° ▶ View Solution
   2. 120° ▶ View Solution
   3. 90° ▶ View Solution
   4. 72° ▶ View Solution
   5. 60° ▶ View Solution
   6. 45° ▶ View Solution
   7. 40° ▶ View Solution
   8. 30° ▶ View Solution

4. Compare Line and Rotational Symmetry

   1. 4 lines of symmetry; order 4 ▶ View Solution
   2. 2 lines of symmetry; order 2 ▶ View Solution
   3. 2 lines of symmetry; order 2 ▶ View Solution
   4. 0 lines of symmetry; order 2 ▶ View Solution
   5. 3 lines of symmetry; order 3 ▶ View Solution
   6. 6 lines of symmetry; order 6 ▶ View Solution

5. Identifying Shapes from Properties

   1. Square ▶ View Solution
   2. Parallelogram ▶ View Solution
   3. Isosceles triangle (or kite) ▶ View Solution
   4. Regular pentagon ▶ View Solution
   5. Circle ▶ View Solution

6. Real World Rotational Symmetry

   1. Order 5; minimum angle 72° ▶ View Solution
   2. Order 5 ▶ View Solution
   3. 90° ▶ View Solution
   4. Regular hexagon; maps onto itself every 60° ▶ View Solution
   5. Order 12; minimum angle 30° ▶ View Solution
   6. 120°; no line symmetry — the arrows rotate but do not reflect ▶ View Solution

7. Find the Order from the Angle

   1. 2 ▶ View Solution
   2. 3 ▶ View Solution
   3. 4 ▶ View Solution
   4. 5 ▶ View Solution
   5. 6 ▶ View Solution
   6. 8 ▶ View Solution
   7. 9 ▶ View Solution
   8. 12 ▶ View Solution

8. Rotational Symmetry — Deeper Thinking

   1. 90°, 180°, 270° ▶ View Solution
   2. 60°, 120°, 180°, 240°, 300° ▶ View Solution
   3. n − 1 angles (multiples of 360° ÷ n, from 1 up to n − 1) ▶ View Solution
   4. Yes — e.g. a parallelogram (order 2, 0 lines of symmetry) ▶ View Solution
   5. Yes — e.g. an isosceles triangle (1 line of symmetry, order 1) ▶ View Solution

9. Symmetry of Composite Designs

   1. Order 6, minimum angle 60° ▶ View Solution
   2. Order 4 ▶ View Solution
   3. Order 6; minimum angle 60° ▶ View Solution
   4. 4-bladed: 90°  |  3-bladed: 120° — 4-bladed has the smaller minimum angle ▶ View Solution

10. Rotational Symmetry in Design and Nature

    1. Yes — 240° is a multiple of 60° ▶ View Solution
    2. Order 15; minimum angle 24° ▶ View Solution
    3. 72° ▶ View Solution
    4. Any valid object, e.g. Australian 50-cent coin (12-sided): order 12, minimum angle 30° ▶ View Solution