Question

1. which types of symmetry does the figure display? select all that apply. a reflectional symmetry across a vertical line b reflectional symmetry across a horizontal line c 120° rotational symmetry d 180° rotational symmetry

Explanation:

• Reflectional symmetry:
• A figure has reflectional symmetry if there is a line (axis of symmetry) such that the part of the figure on one side of the line is the mirror - image of the part on the other side.
• For a vertical line of symmetry: If we draw a vertical line through the center of the figure, the left - hand side of the figure is the mirror image of the right - hand side.
• For a horizontal line of symmetry: If we draw a horizontal line through the center of the figure, the upper - hand side of the figure is the mirror image of the lower - hand side.
• Rotational symmetry:
• The formula for the angle of rotational symmetry is \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of times the figure coincides with itself during a \(360^{\circ}\) rotation.
• When \(n = 2\) (the figure coincides with itself 2 times during a \(360^{\circ}\) rotation), \(\theta=\frac{360^{\circ}}{2}=180^{\circ}\). When we rotate the figure by \(180^{\circ}\) about its center, the rotated figure coincides with the original figure.
• When \(n = 3\), \(\theta=\frac{360^{\circ}}{3} = 120^{\circ}\). But when we rotate the given figure by \(120^{\circ}\) about its center, it does not coincide with the original figure.

Answer:

A. reflectional symmetry across a vertical line, B. reflectional symmetry across a horizontal line, D. \(180^{\circ}\) rotational symmetry.