1. **State the order of rotation and angle of rotation for each figure:** - The order of rotation is the number of times a figure maps onto itself during a full 360° rotation. - The angle of rotation is calculated by dividing 360° by the order of rotation: $$\text{Angle of rotation} = \frac{360^\circ}{\text{Order of rotation}}$$ A (rectangle): Order = 2 (rotates onto itself twice in 360°) Angle = $$\frac{360^\circ}{2} = 180^\circ$$ B (square): Order = 4 Angle = $$\frac{360^\circ}{4} = 90^\circ$$ C (arrow pointing up): Order = 1 (only maps onto itself at 360°) Angle = $$360^\circ$$ D (plus sign): Order = 4 Angle = $$90^\circ$$ E (circle with a pie slice removed): Order = 1 Angle = $$360^\circ$$ F (eight arrows evenly spaced): Order = 8 Angle = $$\frac{360^\circ}{8} = 45^\circ$$ G (downward triangle): Order = 3 Angle = $$\frac{360^\circ}{3} = 120^\circ$$ H (connected two circles): Order = 1 Angle = $$360^\circ$$ I (capital letter A): Order = 1 Angle = $$360^\circ$$ J (three lines joined at center 120° apart): Order = 3 Angle = $$120^\circ$$ 2. **Lines of symmetry and rotational symmetry for given figures:** - Flower with 4 petals: Lines of symmetry = 4 (each petal axis), rotational symmetry order = 4 - Circle with diagonal slash: Lines of symmetry = 1 (the slash line), rotational symmetry order = 1 - 5-pointed star: Lines of symmetry = 5, rotational symmetry order = 5 - Shape with alternating black and white segments (striped circle): Lines of symmetry = depends on segments, assume 2 for simplicity, rotational symmetry order = 2 - Circle with 3 small attached shapes evenly spaced: Lines of symmetry = 3, rotational symmetry order = 3 - Hexagon divided into 6 triangular segments with alternating shading: Lines of symmetry = 6, rotational symmetry order = 6 3. **Draw figures with given lines of symmetry:** - a) Line of symmetry = 8: An octagon or 8-petal flower - b) One diagonal line of symmetry: A right triangle or kite shape - c) Two diagonal lines of symmetry: A square or rectangle with diagonals - d) Line of symmetry = 10: A decagon or 10-petal flower 4. **Angle of rotation for order 5 rotational symmetry:** $$\text{Angle} = \frac{360^\circ}{5} = 72^\circ$$ 5. **Order of rotational symmetry for angle 60°:** $$\text{Order} = \frac{360^\circ}{60^\circ} = 6$$ This completes the worksheet problems on symmetry.