Question

pairs of congruent corresponding angles must be similar.
what does it mean for triangles to be similar?
what does similar mean in geometry?
choose 1 answer:
a if all of the corresponding pairs of angles in two figures are congruent, then the figures are similar.
b if all of the corresponding pairs of sides in two figures have equal ratios, then the figures are similar.
c if we can map one figure onto the other using a sequence of rigid transformations, then the figures are similar.
d if we can map one figure onto the other using a sequence of rigid transformations and dilations, then the figures are similar.

Explanation:

To determine the correct answer, we recall the definition of similar figures in geometry. Similar figures can be mapped onto each other using rigid transformations (translations, rotations, reflections) and dilations (which scale the figure).

• Option A: Only congruent angles aren't sufficient; sides must also be proportional. So A is incorrect.
• Option B: Only proportional sides aren't sufficient; angles must also be congruent. So B is incorrect.
• Option C: Rigid transformations alone give congruent figures, not similar (unless the scale factor is 1). So C is incorrect.
• Option D: This matches the definition of similar figures, as rigid transformations preserve shape and size (congruence) and dilations change size while preserving shape, so combining them allows mapping similar figures.

Answer:

D. If we can map one figure onto the other using a sequence of rigid transformations and dilations, then the figures are similar.