Question

which of the following statements is true?

• if two polygons are similar, then the corresponding sides are proportional and the corresponding angles are proportional.
• if two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent.
• if two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional.
• none of these choices are correct.

Explanation:

Step1: Recall Similar Polygons Definition

Similar polygons have corresponding angles congruent (equal in measure) and corresponding sides proportional (their ratios are equal).

Step2: Analyze Each Option

• First option: Incorrect. Corresponding angles in similar polygons are congruent (equal), not proportional.
• Second option: Correct. Matches the definition of similar polygons (corresponding sides proportional, corresponding angles congruent).
• Third option: Incorrect. Corresponding sides in similar polygons are proportional (not necessarily congruent), and angles are congruent (not proportional).
• Fourth option: Incorrect, since the second option is correct.

Answer:

The second option (the one stating "If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent")