A line of symmetry is a fold line where one half of a figure lands exactly on the other half. Every figure below can be folded. Move the fold line, fold, and see whether the halves match. Questions 1 to 16.
Pick a shape. Turn the fold line with the slider, then tap Fold. The orange half flips over. If it covers the blue half exactly, you found a line of symmetry.
Tap an answer. Then use Fold it to test the shape in the lab above.
How many lines of symmetry does it have? Change the size of the angle, then try folding along different lines.
Answer: 1 line of symmetry, the bisector of the angle. It splits the angle into two equal angles, and the two equal arms fall on each other. This is true for an angle of any size.
Guess the number first. Then fold to test, or tap Show all lines.
A regular polygon with n equal sides has exactly n lines of symmetry. Try the octagon (Q9), the pentagon and the hexagon (Q10), or slide to any number of sides.
Drawn to scale on centimetre squares. Tap Next step and watch each line being drawn, just as you would with ruler, protractor and compasses.
Which of these figures can be folded so the halves match? Test each one.
Answer: (ii), (iii) and (v) have lines of symmetry. (i) and (iv) have none. They only look the same after a half turn, which is point symmetry, the next topic in the chapter.
| Q | Answer |
|---|---|
| 1 | (iii) An isosceles trapezium |
| 2 | 1 line, the bisector of the angle |
| 3 | 0 (no line of symmetry) |
| 4 | (iv) Unequal: square has 4, rectangle has 2 |
| 5 | (ii) Two lines (its diagonals) |
| 6 | (i) No line of symmetry |
| 7 | (i) No line of symmetry |
| 8 | (i) 1 (ii) 1 (iii) 2 (iv) 4 |
| 9 | Regular octagon: 8 lines |
| 10 | (i) Pentagon: 5 lines (ii) Hexagon: 6 lines |
| 11 | Isosceles triangle: 1 line (perpendicular bisector of BC through A) |
| 12 | Right isosceles triangle (AB = BC): 1 line (bisector of ∠B) |
| 13 | Equilateral triangle: 3 lines |
| 14 | Square: 4 lines (2 diagonals, 2 joining midpoints of opposite sides) |
| 15 | Perpendicular bisector of AB, made with compasses |
| 16 | (ii), (iii), (v) have at least one line; (i), (iv) have none |