Question

is the pair of objects congruent? if the pair of objects is congruent, describe a composition of rigid motions that maps one to the other.

Explanation:

Step1: Check Congruence

Both figures are composed of the same set of colored rectangles/squares (same shapes, sizes, and number of each color - based on visual inspection of the components). So they are congruent (rigid motions preserve size/shape, and we can rearrange via rotations/reflections/translations).

Step2: Describe Rigid Motions

1. Rotate the tall pink rectangle 90° clockwise (it becomes the horizontal pink rectangle at the top).
2. Rotate the small blue rectangle 90° counterclockwise (matches the vertical blue on the right).
3. Rotate the small pink rectangle 90° clockwise (matches the vertical pink on the bottom).
4. Rotate the large cyan rectangle 90° counterclockwise (matches the vertical cyan on the right).
5. Translate/rotate the purple square to its position, and the yellow square stays (or adjust via translations after rotations to align all components). Overall, a composition of rotations (and translations) maps one to the other.

Answer:

The pair of objects is congruent. A composition of rigid motions: Rotate the tall pink rectangle 90° clockwise, rotate the small blue rectangle 90° counterclockwise, rotate the small pink rectangle 90° clockwise, rotate the large cyan rectangle 90° counterclockwise, and translate/rotate other components (like the purple square) as needed to align all parts.