Question

which figure has an order 3 rotational symmetry?
○ right triangle
○ equilateral triangle
○ regular hexagon
○ right trapezoid

Explanation:

Step1: Recall the formula for the order of rotational symmetry

The order of rotational symmetry of a regular polygon with \(n\) sides is \(n\). For a non - regular shape, we check the number of times it maps onto itself when rotated \(360^{\circ}\).

Step2: Analyze each option

• Right triangle: A right triangle is not a regular polygon. When rotated \(360^{\circ}\), it maps onto itself only once. So, its order of rotational symmetry is \(1\).
• Equilateral triangle: An equilateral triangle is a regular polygon with \(n = 3\) sides. Using the formula for the order of rotational symmetry of a regular polygon (\(n\)), when we rotate an equilateral triangle by \(\frac{360^{\circ}}{3}=120^{\circ}\), it maps onto itself. And the order of rotational symmetry \(n = 3\).
• Regular hexagon: A regular hexagon is a regular polygon with \(n=6\) sides. Using the formula for the order of rotational symmetry of a regular polygon (\(n\)), when we rotate a regular hexagon by \(\frac{360^{\circ}}{6} = 60^{\circ}\), it maps onto itself. And the order of rotational symmetry \(n = 6\).
• Right trapezoid: A right trapezoid is not a regular polygon. When rotated \(360^{\circ}\), it maps onto itself only once. So, its order of rotational symmetry is \(1\).

Answer:

equilateral triangle