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.
<span>Rigid transformations (translations, reflections and rotations) are transformations that maintain the measure of line segments and angles. Being able to map a pre-image to an image using rigid transformations means that the sides are the same length, as is the angle between the two.</span>
