To find the inverse of the given statement, we need to understand what an inverse of a conditional statement entails. The general form of a conditional statement is:
If P, then Q.
The inverse of this statement is formed by negating both the hypothesis (P) and the conclusion (Q):
If not P, then not Q.
Let's apply this process step-by-step to the given statement:
1. Identify the hypothesis (P) and the conclusion (Q) in the original statement:
- Original statement: "If the alternate interior angles are congruent, then the lines are parallel."
- Hypothesis (P): "The alternate interior angles are congruent."
- Conclusion (Q): "The lines are parallel."
2. Form the inverse by negating both the hypothesis and the conclusion:
- Negate the hypothesis: "The alternate interior angles are not congruent."
- Negate the conclusion: "The lines are not parallel."
3. Combine the negated hypothesis and conclusion to form the inverse statement:
- Inverse statement: "If the alternate interior angles are not congruent, then the lines are not parallel."
Therefore, the inverse of the given statement is:
If the alternate interior angles are not congruent, then the lines are not parallel.
