Answer:
Two shapes have corresponding congruent parts if and only if the shapes are congruent and one shape can be mapped to the other using a series of rigid transformations. (The first option)
Explanation:
The other three statements are false.
Two shapes can have corresponding congruent parts without being congruent. For example, a square and a rectangle can have congruent sides, but they are not congruent shapes.
Two shapes can be congruent without being able to be mapped to each other using a series of rigid transformations. For example, a sphere and a cube are congruent shapes, but they cannot be mapped to each other using only rigid transformations.
Two shapes can be non-congruent and be able to be mapped to each other using a series of rigid transformations. For example, a square and a rectangle can be mapped to each other using a combination of a rotation and a translation.