One proof of the SAS criterion for triangle congruece relies on the "rigid motion" (isometry) definition of congruent figures and the properties of rigid motions in the plane. See this video for an animated walk through of the argument.
At 1:46, the video states that "basic rigid motions preserve degrees in angles." The proofs that I have seen of this statement assume SAS in the first place.
Is it possible to prove that a rigid motion in the plane maps angles to angles with the same measure, without assuming SAS? If so, is there a source that presents such a proof?