Question

in similar polygons, corresponding sides are _ and corresponding angles are _. (fill in the blanks) proportional, proportional; congruent, proportional; congruent, congruent; proportional, congruent

Explanation:

To solve this, we recall the definition of similar polygons. By definition, in similar polygons, corresponding sides are proportional (their ratios are equal) and corresponding angles are congruent (equal in measure). We check each option:

• Option 1: "proportional, proportional" is incorrect because angles in similar polygons are congruent, not proportional.
• Option 2: "congruent, proportional" is incorrect as sides are proportional and angles are congruent (this option swaps the properties).
• Option 3: "congruent, congruent" is incorrect because sides in similar polygons are proportional (congruent sides would be for congruent polygons, not just similar).
• Option 4: "proportional, congruent" matches the definition of similar polygons (sides are proportional, angles are congruent).

Answer:

D. proportional, congruent (assuming the last option is labeled D; if the options are labeled as per the order: the fourth option "proportional, congruent")