Why does a rectangle have only two reflection symmetries?

[LagrangeEuler]

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

 

[fresh_42]

What happens if you reflect a rectangle with two different side lengths at one of its diagonal?

 

[LagrangeEuler]

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?

 

[fresh_42]

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?

 

[LagrangeEuler]

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.

 

[dkotschessaa]

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

The key word is "symmetry."

 

[dkotschessaa]

Have you tried these physically with a piece of paper?

 

[fresh_42]

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.)

 

[LagrangeEuler]

Thanks a lot Sir for your help.