Question

Which of the following statements are true?

Answer 1

Answer:

II, III, and IV

Step-by-step explanation:

Define:

Similar polygons:

• Corresponding angles are equal
• Corresponding sides are in a constant proportion

Congruent polygons:

• Corresponding angles are equal
• Corresponding sides are equal

Let's break each statement down one-by-one:

I. Corresponding sides of similar figures are the same.

False - Corresponding sides of similar figures are in a constant proportion, but not necessarily the same. Congruent figures have equal corresponding sides, but similar figures only have their corresponding sides in a constant proportion.

II. Corresponding sides of congruent figures are the same.

True - By definition, corresponding figures have equal sides and angles. Therefore, this statement is true.

III. Corresponding angles of congruent figures are the same.

True - By definition, corresponding figures have equal sides and angles. Therefore, this statement is true.

IV. Corresponding angles of similar figures are the same.

True - While corresponding sides of similar figures may not be the same, their angles are. This is what gives them the similar characteristic. All similar polygons have equal angles, therefore this statement is true.