What is a reflexive property in geometry?

Reflexive properties in geometry describe geometric shapes that are symmetrical to themselves so they can be rotated over 180 degrees without changing the shape.

For example, a circle is reflexive because it has radial symmetry and rotational symmetry. It also doesn’t matter how you rotate the circle, it will always produce another circle. The most well-known way to think about symmetry is the idea of a mirror image: If you look at yourself in a mirror, your reflection should look just like you. So if you were right handed before looking at yourself in the mirror; after looking at your reflection, your left hand should now become your dominant one as it would appear that way on top of your right side when looking at your reflection.

A square also has reflexive properties because it has 90 degree rotational symmetry and it’s the only shape that you can perfectly tile. But a square does not have any radial symmetry so it’s not symmetrical to itself when rotated.