Question

which of the following statements best describes similar polygons?
a two polygons are similar if all the corresponding angles are congruent or all the corresponding sides are congruent.
b two polygons are similar if all the corresponding angles are proportional and all the corresponding sides are congruent.
c two polygons are similar if all the corresponding angles are congruent and all the corresponding sides are proportional.
d two polygons are similar if all the corresponding angles are proportional and all the corresponding angles are proportional.
e two polygons are similar if all the corresponding angles are congruent or all the corresponding sides are proportional.

Explanation:

For two polygons to be similar, the key requirements are that all corresponding angles are congruent (equal in measure) and all corresponding sides are proportional (have the same ratio).

• Option A: The use of "or" is incorrect. Both angle and side - related conditions (not just one) are needed for similarity. Also, congruent sides would make them congruent (a special case of similarity with a scale factor of 1), but the general similarity does not require side congruence.
• Option B: Angles should be congruent, not proportional. And sides should be proportional, not congruent for non - congruent similar polygons.
• Option C: This is correct as per the definition of similar polygons.
• Option D: Repeating "angles are proportional" is incorrect. Angles should be congruent.
• Option E: The "or" condition is wrong. Both angle congruence and side proportionality are required.

Answer:

C. Two polygons are similar if all the corresponding angles are congruent and all the corresponding sides are proportional.