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.

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