To find the inverse of a given conditional statement, you need to negate both the hypothesis and the conclusion while keeping the same logical structure.
Given the statement:
"If the corresponding angles are congruent, then the lines are parallel."
1. Identify the hypothesis and conclusion:
- Hypothesis (P): "the corresponding angles are congruent"
- Conclusion (Q): "the lines are parallel"
2. Form the inverse by negating both the hypothesis and conclusion:
- Negation of the hypothesis (¬P): "the corresponding angles are not congruent"
- Negation of the conclusion (¬Q): "the lines are not parallel"
3. Construct the inverse statement:
- "If the corresponding angles are not congruent, then the lines are not parallel."
Thus, the inverse of the statement "If the corresponding angles are congruent, then the lines are parallel." is:
"If the corresponding angles are not congruent, then the lines are not parallel."
So, the correct answer is:
"If the corresponding angles are not congruent, then the lines are not parallel."
