1. The problem asks about the relationship between the side lengths of Triangles 1 and 2 under a rigid transformation. 2. A rigid transformation preserves distances and angles, so the side lengths of Triangle 1 and Triangle 2 must be the same. 3. Therefore, the correct choice is C: The side lengths are the same. 4. Next, for Triangle 3, since it is also obtained from Triangle 1 by a rigid transformation, its side lengths are the same as Triangle 1. 5. This is because rigid transformations include rotations, reflections, and translations, none of which change side lengths. 6. Finally, for the question about the areas of all eight triangles in the flag, since all are related by rigid transformations, their areas are preserved. 7. Hence, all eight triangles have the same area. 8. This is because area is preserved under rigid transformations, which do not involve scaling. Final answers: - Side lengths of Triangles 1 and 2: same. - Side lengths of Triangle 3: same as Triangle 1. - All eight triangles have the same area.