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2. do rectangles have rotational symmetry? do rectangles have reflectional symmetry? explain.

Question

2. Do rectangles have rotational symmetry? Do rectangles have reflectional symmetry? Explain.

Solution

Verificación de expertos
4.5 (262 Votos)
Thiago Mestre · Tutor por 5 anos

Resposta

Yes, rectangles have both rotational symmetry and reflectional symmetry. Let me explain each in detail:### 1. **Rotational Symmetry**:A rectangle has rotational symmetry of order **2**. This means that if you rotate a rectangle by **180 degrees** around its center, it will look exactly the same as it did before the rotation. However, rotating it by any other angle (other than multiples of 180°) will not result in the same appearance.- For example, if you rotate a rectangle by 90° or 270°, it will not align with its original position unless it is a square (a special type of rectangle).### 2. **Reflectional Symmetry**:A rectangle has **reflectional symmetry** because it can be divided into two identical halves along certain lines of symmetry. Specifically, a rectangle has **two lines of reflectional symmetry**: - One line of symmetry runs vertically through the center of the rectangle, dividing it into two equal left and right halves. - The other line of symmetry runs horizontally through the center of the rectangle, dividing it into two equal top and bottom halves.### Summary:- Rectangles have **rotational symmetry of order 2** (180° rotation).- Rectangles have **two lines of reflectional symmetry** (vertical and horizontal axes). This combination of symmetries is one of the defining characteristics of rectangles.