Lucia draws a square and plots the center of a square. She claims that any rotation about the center of the square that is multiple of 45° will caryy the square onto itself.

1) Considering that the rotation angle about the center of the square that rotates it onto itself is 90º.
2) Then examining the options we can state:
Lucia's claim is incorrect since not all rotations that are multiple of 45º carry a square onto itself
Because, for example, a rotation of 135