Final answer:
After evaluating the statements, corresponding angles are indeed the same for both congruent and similar figures, and corresponding sides are the same for congruent figures, but only proportional for similar figures. Thus, statements (i), (ii), and (iii) are true, making Option D (I, II, and III) the correct answer.
Step-by-step explanation:
When evaluating the statements provided about figures in geometry, we can determine the following:
- Corresponding angles of congruent figures are indeed the same (equal in measure).
- Corresponding angles of similar figures are also the same (equal in measure).
- Corresponding sides of congruent figures are the same (equal in length).
- However, corresponding sides of similar figures are proportional, not necessarily the same length. They are the same in ratio to one another.
With these clarifications, we can deduce that statements (i), (ii), and (iii) are true, while statement (iv) is only partially true—it would be more accurate to say the sides are proportional rather than the same. Therefore, the correct answer is:
Option D: I, II, and III