Layla didn't use only rigid transformation, so the figures are not congruent.
Explanation:
Rigid transformation is the procedure required to change the orientation of a given figure, without resizing it. Examples are translation, reflection, and rotations.
Since the mapping was achieved using a translation and dilation, there is an error in her conclusion.
Dilation is the process of resizing a given figure but preserving its shape. It preserves the angles and the shape of the figure, but not the length of the sides.
Dilation is not an example of rigid transformation, therefore she did not only use rigid transformation to map circle M onto circle N.