Final answer:
A rigid transformation is the movement of a shape that preserves both the size and shape, meaning that the lengths of sides and angles remain unchanged. Rotations, translations, and reflections are all examples of rigid transformations, and the result is that the shape's pre-image and image are congruent.
Step-by-step explanation:
A rigid transformation refers to the movement of a shape in such a way that its size and shape are not changed. Therefore, the correct answer to this question is: A) The length of the side and the angles stay the same as the shape moves.
Rigid transformations include rotations, translations (sliding), and reflections (flipping). During a rigid transformation, the pre-image and image are always congruent, meaning they have the same size and shape. For example, when you rotate a cube 90° around an axis perpendicular to any pair of its six faces or 120° around an axis that extends between opposite corners, the cube's appearance does not change, demonstrating its rigidness.
Another example of a rigid transformation would be a point (x, y) in a coordinate system remaining at the same distances from other points despite the coordinate system being rotated to become a new coordinate system S'. Therefore, Answer E) 'As a shape moves to a new location, it is congruent to the original shape' is also correct.