Alon was curious if segments \overline{JK} JK start overline, J, K, end overline and \overline{NM} NM start overline, N, M, end overline were congruent, so he tried to map one figure onto the other using transformations: Alon concluded: "It's not possible to map \overline{JK} JK start overline, J, K, end overline onto \overline{NM} NM start overline, N, M, end overline using a sequence of rigid transformations, so the segments are not congruent." What error did Alon make in his conclusion?
