Point symmetry, rotational symmetry, and all three types side by side. Then worked solutions to Exercise 19B, 19C, Mental Maths, Assertion–Reason and the competency questions. Every figure can be turned on screen.
A figure has point symmetry about a centre O if, for every point P on it, there is a point P′ on the figure directly opposite, on the other side of O, with OP = OP′. Another way to see it: the figure looks exactly the same after a half turn (180°).
Slide P along the figure. Watch where P′ lands. Then tap Half turn.
A figure has rotational symmetry if it fits onto itself more than once while it is turned through 360°. If A° is the smallest turn that makes it fit, then order = 360 ÷ A. For rotational symmetry, A must be 180° or less.
The orange copy turns over the blue figure. Drag the slider, or tap Play full turn and count how many times it fits. The dial marks each fit.
Pick a figure, guess the three answers, then run the tests. Lines draws every line of symmetry. Half turn checks point symmetry. Full turn finds the order of rotation.
A shortcut that always works: a figure has point symmetry exactly when it fits after a half turn, so its order of rotation is an even number (2, 4, 6…). Order 3 or 5 means no point symmetry.
State the type(s) of symmetry possessed by each figure. Explain each type.
Tap an answer. Use See it to test the figure on the turntable.
Decide two things separately: is A true? Is R true? Only then ask whether R explains A.
| Question | Answer |
|---|---|
| 19B Q1 | (ii) A semicircle |
| 19B Q2 | (iv) A rectangle |
| 19B Q3 | (ii) One line of symmetry |
| 19B Q4 | (i) point, rotation 4 · (ii) point, rotation 2 · (iii) 1 line · (iv) 3 lines, rotation 3 · (v) 1 line · (vi) 2 lines, point, rotation 2 · (vii) 1 line · (viii) point, rotation 2 · (ix) 2 lines, point, rotation 2 · (x) 3 lines, rotation 3 |
| 19C 1–5 | (d) · (a) · (b) · (d) · (d) |
| 19C 6–10 | (a) · (a) · (c) · (a) · (c) |
| 19C 11–15 | (a) · (b) · (a) · (b) · (c) |
| Fill in | infinitely many · line (linear) · perpendicular bisector · two · square |
| True/False | T · T · T · F · F |
| A–R | 1 (d) · 2 (c) |
| Competency | 1 (c) · 2 (c) · 3 (b) · 4 (a) |