LagrangeEuler said:Why group of symmetry of rectangle does not have more reflections but only two. Why does not have reflections over diagonal as in case of square? Thanks for the answer.
http://mathonline.wikidot.com/the-group-of-symmetries-of-a-rectangle
Yes, that's true. But what happens if you add an orientation, a tiny arrow which shows a direction you could walk along the rectangle? Then you see, that rotation and reflection are different, although the non-oriented figure is the same. (Not important to your original question though, but useful to remember.)LagrangeEuler said:I don't not why
http://mathonline.wikidot.com/the-group-of-symmetries-of-a-rectangle
If I look figure here rotation by 180 degrees will be symmetry.
The Group of Symmetry of Rectangle is the set of all possible symmetries that can be applied to a rectangle. These symmetries include rotations, reflections, and translations.
There are a total of 8 symmetries in the Group of Symmetry of Rectangle. This includes 4 rotations (90°, 180°, 270°, and 360°), 2 reflections (horizontal and vertical), and 2 translations (moving left or right and up or down).
A reflection symmetry in a rectangle is when the rectangle is flipped over a line, called the line of symmetry, and the resulting shape is identical to the original shape. In a rectangle, there are two possible reflection symmetries - horizontal and vertical.
The diagonals of a rectangle are related to the Group of Symmetry as they are used to determine the rotation symmetries. The two diagonals of a rectangle are also lines of symmetry. This means that if a rectangle is rotated 180°, it will look the same as before the rotation.
No, a rectangle can only have 8 symmetries in its Group of Symmetry. This is because a rectangle has four sides and four corners, and each symmetry in the Group of Symmetry can only be applied once. Therefore, there are only 8 possible symmetries for a rectangle.