Symmetry — Review Answers

1. Lines of Symmetry

   1. 8 ▶ View Solution
   2. 1 ▶ View Solution
   3. 0 ▶ View Solution
   4. 4 ▶ View Solution
   5. 1 ▶ View Solution
   6. 0 ▶ View Solution
   7. 7 ▶ View Solution
   8. 2 ▶ View Solution

2. Rotational Symmetry

   1. Order 8, minimum angle 45° ▶ View Solution
   2. Order 2, minimum angle 180° ▶ View Solution
   3. Order 3, minimum angle 120° ▶ View Solution
   4. Order 2, minimum angle 180° ▶ View Solution
   5. Infinite order — looks the same after any angle of rotation ▶ View Solution
   6. Order 1 (no rotational symmetry) ▶ View Solution

3. Line vs Rotational

   1. 0 lines of symmetry; order 2 ▶ View Solution
   2. 2 lines of symmetry; order 2 ▶ View Solution
   3. 5 lines of symmetry; order 5 ▶ View Solution
   4. 1 line of symmetry; order 1 (no rotational symmetry) ▶ View Solution
   5. 4 lines of symmetry; order 4 ▶ View Solution

4. Mixed Problems

   1. Equilateral triangle ▶ View Solution
   2. Rectangle and rhombus ▶ View Solution
   3. 40° ▶ View Solution
   4. False — an isosceles triangle has 1 line of symmetry but no rotational symmetry (order 1) ▶ View Solution

5. Problem Solving

   1. Square and regular octagon ▶ View Solution
   2. Order 8; yes — rotating 45° gives the same appearance ▶ View Solution
   3. When rotated 180° a parallelogram maps onto itself, but there is no fold line that creates equal mirror halves — so it has no line symmetry ▶ View Solution
   4. (−3, 2) ▶ View Solution

6. Alphabet Symmetry

   1. 2 (horizontal and vertical) ▶ View Solution
   2. 1 (vertical) ▶ View Solution
   3. 0 ▶ View Solution
   4. Infinite (every diameter is a line of symmetry) ▶ View Solution
   5. S, Z, N (order 2 rotational symmetry, no line symmetry) ▶ View Solution

7. Lines of Symmetry in Regular Polygons

   1. 3 ▶ View Solution
   2. 6 ▶ View Solution
   3. 10 ▶ View Solution
   4. A regular polygon with n sides has exactly n lines of symmetry ▶ View Solution

8. Rotational Symmetry in Real Life

   1. Order 4; minimum angle 90° ▶ View Solution
   2. 60° ▶ View Solution
   3. Student response — e.g. a wheel (order infinite) and a clock face without numbers (order 12) ▶ View Solution

9. Create Symmetric Designs

   1. Student response — e.g. a rectangle (2 lines of symmetry along horizontal and vertical axes; order 2 rotational symmetry) ▶ View Solution
   2. Yes — e.g. a parallelogram (order 2, 0 lines of symmetry) ▶ View Solution
   3. Yes — e.g. an isosceles triangle (1 line of symmetry, order 1) ▶ View Solution

10. Symmetry in Coordinates

    1. (−3, 5) ▶ View Solution
    2. (−2, −4) ▶ View Solution
    3. Yes — the vertical line x = 4 is a line of symmetry; (2, 0) and (6, 0) are equidistant from it, and (4, 5) lies on it ▶ View Solution