Question

what types of symmetry does the figure show?

Explanation:

Step1: Check for rotational symmetry

Rotational symmetry means the figure looks the same after a rotation. If we rotate this figure by \(120^{\circ}\) (since \(360\div3 = 120\)), it will map onto itself.

Step2: Check for line - symmetry

Line symmetry (reflection symmetry) means there is a line (axis) such that the figure is symmetric about that line. This figure has 3 lines of symmetry (passing through each vertex and the mid - point of the opposite side).

Answer:

The figure shows rotational symmetry (with a rotation of \(120^{\circ}\)) and line symmetry (3 lines of symmetry).