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

Brief Explanations:

Rigid - transformations (translations, rotations, reflections) preserve side - lengths and angle - measures. To justify SAS congruence, we can use rigid transformations to map one triangle onto another. If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, we can use a sequence of rigid transformations to align the corresponding parts. First, we can translate one triangle so that one pair of corresponding congruent sides coincide. Then, we can rotate the triangle about the common vertex of the congruent sides so that the included angles coincide. Since rigid transformations preserve side - lengths and angle - measures, the other pair of congruent sides will also coincide, showing the two triangles are congruent.

Answer:

Rigid transformations are used to map one triangle onto another. First, translate to align one pair of congruent sides. Then, rotate about the common vertex to align the included angles. Since rigid transformations preserve side - lengths and angle - measures, the triangles are congruent.