Question

a figure has rotational symmetry if a rotation of 180° or less produces an image that fits exactly on the original figure. determine whether the design on the figures has rotational symmetry. explain your reasoning.
7)
8)

Explanation:

Step1: Analyze rotational symmetry concept

Rotational symmetry means a figure looks the same after a rotation of \(180^{\circ}\) or less.

Step2: Examine the first figure (7)

The circular figure has multiple repeating patterns. If we rotate it by \(60^{\circ}\) (since \(360\div6 = 60\)), the image coincides with the original. So it has rotational symmetry.

Step3: Examine the second figure (8)

The square - patterned figure. If we rotate it by \(180^{\circ}\), the shaded and un - shaded parts, and the geometric shapes' positions relative to each other, coincide with the original. So it has rotational symmetry.

Answer:

1. The figure has rotational symmetry. When rotated by \(60^{\circ}\) (as \(360\div6=60\)), the image matches the original.
2. The figure has rotational symmetry. When rotated by \(180^{\circ}\), the image matches the original.