How does the criteria for triangle congruence (asa, sas, and sss) follow from the definition of congruence in terms of rigid motions?

A rigid motion is a transformation of a figure which does not change shape and the size of the original figure.

i.e. It preserves the side-length and measure of interior angles of a figure.

Thus , if we use rigid motions to transform a triangle then all the corresponding side-lengths and  measure of interior angles of a figure remains exactly same.

That' how ,the criteria for triangle congruence (ASA, SAS, and SSS) directly follow from the definition of congruence in terms of rigid motions.

ian gonna lie that is way to much