# Group of Symmetry of Rectangle: Reflections & Diagonals

• B
• LagrangeEuler
In summary, the group of symmetries of a rectangle only has two reflections because if you reflect the rectangle over its diagonal, the sides will change and it will no longer be symmetrical. This is different from the case of a square where reflections over the diagonal are possible. Additionally, rotation also makes a difference in the orientation of the rectangle.
What happens if you reflect a rectangle with two different side lengths at one of its diagonal?

They change sides I suppose. So when I did that transformation longer side if it was horizontal it will be vertical after that transformation. Right?

Yes. If it was first lying down, the it's standing up afterwards, so it changed. This doesn't happen if you reflect it along the half sections parallel to the borders. By the way, rotation also makes a difference, even if rotated by ##180°##. Do you know why?

Have you tried these physically with a piece of paper?

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.
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.)

Thanks a lot Sir for your help.

Last edited:

## 1. What is the Group of Symmetry of Rectangle?

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.

## 2. How many symmetries are in the Group of Symmetry of Rectangle?

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).

## 3. What is a reflection symmetry in a rectangle?

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.

## 4. How are diagonals related to the Group of Symmetry of Rectangle?

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.

## 5. Can a rectangle have more than 8 symmetries?

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.

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