How are rigid transformations used to justify the sas congruence theorem?

Rigid transformations preserve segment lengths and angle measures. If you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. To prove SAS, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. Then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the SAS congruence theorem.

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