Final answer:
Two figures are congruent if their corresponding sides and angles are congruent. Dilations result in similar but not congruent figures and proportional sides indicate similarity instead of congruence.
Step-by-step explanation:
For two figures to be congruent, they must have the same shape and size, even if one is a flipped or rotated version of the other. We can establish congruence through a couple of criteria:
- a. Corresponding Sides are Congruent: Every side in one figure must be of the same length as the corresponding side in the other figure.
- b. Corresponding Angles are Congruent: Every angle in one figure must have the same measure as the corresponding angle in the other figure.
However, these other options do not apply to congruent figures:
- c. One figure is a dilation of the second: A dilation might change the size of the figure, which would mean the figures are similar, not congruent.
- d. Corresponding Sides are Proportional: This is a criterion for similarity, not congruence. 'Proportional' implies that sides can have different lengths, which would not qualify for congruence.