Question

what is the definition of congruence? a. if two figures have the same shape, then they are congruent. b. if two figures have the same area, then they are congruent. c. if there is a sequence of transformations taking one figure to another, then they are congruent. d. if there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.

Explanation:

Congruent figures are defined as figures for which there exists a sequence of rigid - motions (rotations, reflections, and translations) that can map one figure onto the other. Having the same shape is not enough (similar figures have the same shape but may not be congruent), and having the same area does not imply congruence. A general sequence of transformations may include non - rigid ones like dilations which would not result in congruence.

Answer:

D. If there is a sequence of rotations, reflections, and translations that take one figure to the other, then they are congruent.