The group of symmetries of a rectangle includes only two reflections: across the vertical and horizontal midlines. Unlike a square, a rectangle does not possess reflections over its diagonals due to the unequal side lengths, which alter the orientation of the rectangle upon reflection. Additionally, a 180° rotation is a symmetry operation for rectangles, but it differs from reflection as it maintains the orientation of the figure. Understanding these properties is crucial for comprehending geometric symmetry.
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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.