Answer:
Let's analyze the given statements in terms of their converses, inverses, and contrapositives:
1. **Statement:** If two angles form vertical angles, then they are congruent.
- **Converse:** If two angles are congruent, then they form vertical angles.
- **Inverse:** If two angles do not form vertical angles, then they are not congruent.
- **Contrapositive:** If two angles are not congruent, then they do not form vertical angles.
2. **Statement:** If you are a second-year high school student, then you are a sophomore.
- **Converse:** If you are a sophomore, then you are a second-year high school student.
- **Inverse:** If you are not a second-year high school student, then you are not a sophomore.
- **Contrapositive:** If you are not a sophomore, then you are not a second-year high school student.
These examples illustrate the concepts of converses, inverses, and contrapositives in conditional statements. The converse switches the hypothesis and conclusion, the inverse negates both the hypothesis and conclusion, and the contrapositive is a combination of these changes.
