Question

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

Explanation:

Step1: Recall the formula for rotational symmetry order

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 coincides with its original position when rotated \(360^{\circ}\).

Step2: Analyze each option

• Right triangle: A right triangle is not a regular polygon. When rotated \(360^{\circ}\), it coincides with its original position 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 rotated \(360^{\circ}\), it coincides with its original position \(3\) times (\(360\div120 = 3\), since the angle of rotation for an equilateral triangle is \(120^{\circ}\)).
• Regular hexagon: A regular hexagon is a regular polygon with \(n=6\) sides. When rotated \(360^{\circ}\), it coincides with its original position \(6\) times (\(360\div60 = 6\), since the angle of rotation for a regular hexagon is \(60^{\circ}\)).
• Right trapezoid: A right trapezoid is not a regular polygon. When rotated \(360^{\circ}\), it coincides with its original position only once. So, its order of rotational symmetry is \(1\).

Answer:

equilateral triangle