A shape has rotational symmetry whereby it has the same appearance when it is rotated partially, and a line of symmetry cuts an object into two matching halves
The correct values are as follows;
1. a. The figure has four lines of symmetry
b. The figure has six lines of symmetry
c. The figure has five lines of symmetry
d. the figure has two lines of symmetry
2. The error is that rotational symmetry of a octagon are 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°
3. a. 90°, 180°, and 270°
b. 120° and 240°
Reasons:
1. a. The lines of symmetry of the figure are;
- A diagonal inclined 45° to the horizontal
- A diagonal inclined at 135° to the horizontal
Therefore;
- The figure has four lines of symmetry, the correct option is option a.
b. The figure is a regular hexagon and it has six lines of symmetry
- The figure has six lines of symmetry
c. A star has five lines of symmetry
Therefore;
- The figure has five lines of symmetry
d. A rhombus has two lines of symmetry
- The figure has two lines of symmetry
2. The error is that rotational symmetry of a octagon are 45°, 90°, 135°, 180°, 225°, 270°, 315°, 360°
3. a. The lines of symmetry are perpendicular, therefore, the figure has rotational symmetry of 90°, 180°, and 270°
b. The triangle has three lines of symmetry, therefore, the rotational symmetry are [tex]\dfrac{360^{\circ}}{3} = 120^{\circ}[/tex] apart, therefore
The angles of rotational symmetry are; 120° and 240°
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