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

Ask by Brewer Ray. in the United States
Jan 23,2025

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Answer

Both the isosceles trapezoid and the rhombus have the same rotational symmetry as a rectangle.

Solution

A rectangle has an **order of rotational symmetry of 2**, meaning it looks the same twice during a 360-degree rotation (specifically at 0° and 180°). Let's evaluate each of the given figures: 1. **Isosceles Trapezoid** - **Rotational Symmetry Order:** 2 - **Explanation:** When rotated 180°, an isosceles trapezoid maps onto itself, similar to a rectangle. 2. **Regular Octagon** - **Rotational Symmetry Order:** 8 - **Explanation:** A regular octagon maps onto itself eight times during a full rotation, at every 45° increment. 3. **Square** - **Rotational Symmetry Order:** 4 - **Explanation:** A square maps onto itself four times during a full rotation, at every 90° increment. 4. **Rhombus** - **Rotational Symmetry Order:** 2 - **Explanation:** Like a rectangle, a rhombus maps onto itself twice during a full rotation, at 0° and 180°. **Conclusion:** Both the **isosceles trapezoid** and the **rhombus** have the same order of rotational symmetry (order 2) as a rectangle. Answer: Both the isosceles trapezoid and the rhombus have the same rotational symmetry order as a rectangle.

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A rectangle has rotational symmetry of order 2, meaning it can be rotated 180 degrees and look the same. Interestingly, an isosceles trapezoid also exhibits this type of symmetry, as rotating it halfway will reveal the same shape. So, if you're ever designing a funky trapezoid, just remember that a little spin could showcase its beauty! On the other hand, a square stands tall with an order of rotational symmetry of 4—rotating it 90 degrees or 180 degrees will still keep it looking sharp. Meanwhile, the regular octagon is even more exciting with an order of 8, while a rhombus shares the same order of 2 as the rectangle, but it must rotate a full 180 degrees to look the same! Wouldn’t it be fun to throw a shape party to see these rotations in action?

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