Line Symmetry — Solutions

1. Lines of Symmetry — Shapes

   1. 3 ▶ View Solution
   2. 4 ▶ View Solution
   3. 2 ▶ View Solution
   4. 0 ▶ View Solution
   5. 2 ▶ View Solution
   6. 6 ▶ View Solution
   7. 1 ▶ View Solution
   8. Infinite (∞) ▶ View Solution

2. Classifying Letters

   1. Exactly 1 line of symmetry: A, B, C, M, T, Y ▶ View Solution
   2. 0 lines of symmetry: N, S, Z ▶ View Solution
   3. 2 or more lines of symmetry: H (2 lines), X (2 lines), O (infinite lines) ▶ View Solution

3. True or False

   1. False — a square has 4 lines of symmetry ▶ 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. False — a scalene triangle has 0 lines of symmetry ▶ View Solution
   7. True ▶ View Solution
   8. False — folding along a diagonal does not map corners onto corners ▶ View Solution

4. Rectangles vs Squares

   1. Folding along the diagonal leaves corners unmatched — they overhang rather than meeting ▶ View Solution
   2. Yes — all sides are equal, so corners match exactly when folded along either diagonal ▶ View Solution
   3. The two diagonals (through opposite corners) ▶ View Solution
   4. True — a square always has more lines of symmetry (4) than a non-square rectangle (2) ▶ View Solution

5. Finding Reflected Vertices

   1. (4, 0), (4, 3), (2, 3), (2, 0) ▶ View Solution
   2. Rectangle ▶ View Solution
   3. 2 ▶ View Solution
   4. (3, 0), (3, 4), (1, 2) ▶ View Solution

6. Symmetry in the Real World

   1. No ▶ View Solution
   2. Equilateral triangle ▶ View Solution
   3. (−2, 5) ▶ View Solution
   4. Any two valid examples, e.g. McDonald’s arches (1 line), Star of David (6 lines) ▶ View Solution
   5. 2 lines: rectangle  |  3 lines: equilateral triangle  |  5 lines: regular pentagon ▶ View Solution

7. Lines of Symmetry — Regular Polygons Pattern

   1. 3 sides: 3 lines of symmetry ▶ View Solution
   2. 4 sides: 4 lines of symmetry ▶ View Solution
   3. 5 sides: 5 lines of symmetry ▶ View Solution
   4. 6 sides: 6 lines of symmetry ▶ View Solution
   5. 7 sides: 7 lines of symmetry ▶ View Solution
   6. 8 sides: 8 lines of symmetry ▶ View Solution
   7. 9 sides: 9 lines of symmetry ▶ View Solution
   8. 10 sides: 10 lines of symmetry ▶ View Solution

8. Completing Symmetric Shapes

   1. Isosceles triangle; 1 line of symmetry ▶ View Solution
   2. Full circle; infinitely many lines of symmetry ▶ View Solution
   3. Rectangle; 2 lines of symmetry ▶ View Solution
   4. Kite; 1 line of symmetry ▶ View Solution

9. Lines of Symmetry — Sorting and Reasoning

   1. 0 lines: scalene triangle, parallelogram  |  1 line: isosceles triangle, kite  |  2 lines: rectangle, rhombus  |  More than 2: square (4), equilateral triangle (3), regular hexagon (6), circle (∞) ▶ View Solution
   2. No — quadrilaterals can have 0, 1, 2, or 4 lines of symmetry; 3 is not possible ▶ View Solution
   3. Regular octagon ▶ View Solution
   4. In a rectangle, unequal sides mean corners don’t meet when folded along the diagonal; in a square, all sides are equal so corners map exactly onto each other ▶ View Solution

10. Symmetry Design Challenge

    1. Square (4 lines: horizontal midline, vertical midline, and two diagonals) ▶ View Solution
    2. 2 ▶ View Solution
    3. Yes ▶ View Solution
    4. House-shaped pentagon (rectangle with a centred triangular roof); 1 vertical line of symmetry ▶ View Solution