Question

which figure has the same order of rotational symmetry as a rectangle?
isosceles trapezoid
regular octagon
square
rhombus

Explanation:

Step1: Recall the order of rotational symmetry of a rectangle

A rectangle has an order of rotational symmetry of \(2\). It looks the same when rotated by \(180^{\circ}\) (i.e., \(360\div2 = 180\)).

Step2: Analyze each option

• Isosceles trapezoid:

An isosceles trapezoid has an order of rotational symmetry of \(1\). It only looks the same when rotated by \(360^{\circ}\) (since it is not symmetric in a non - full - rotation way around its center).

• Regular octagon:

The formula for the order of rotational symmetry of a regular \(n\) - sided polygon is \(n\). For a regular octagon (\(n = 8\)), the order of rotational symmetry is \(8\) (\(360\div45=8\), where \(45^{\circ}=\frac{360^{\circ}}{8}\)).

• Square:

For a square (\(n = 4\) in the formula for a regular \(n\) - sided polygon), the order of rotational symmetry is \(4\) (\(360\div90 = 4\), where \(90^{\circ}=\frac{360^{\circ}}{4}\)).

• Rhombus:

A rhombus has an order of rotational symmetry of \(2\). It looks the same when rotated by \(180^{\circ}\) (i.e., \(360\div2=180\)).

So, the rhombus has the same order of rotational symmetry as a rectangle.

Answer:

D. rhombus