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