To find the inverse of a conditional statement, we need to negate both the hypothesis and the conclusion of the original statement.
The original statement is:
"If two lines do not intersect, then the two lines are parallel lines."
Step-by-step process:
1. Identify the hypothesis and the conclusion:
- Hypothesis: Two lines do not intersect.
- Conclusion: Two lines are parallel lines.
2. Negate both the hypothesis and the conclusion:
- Negation of "two lines do not intersect" is "two lines intersect."
- Negation of "two lines are parallel lines" is "two lines are not parallel lines."
3. Write the inverse statement by combining the negations:
- Inverse statement: "If two lines intersect, then the two lines are not parallel."
Now, let's compare the inverse statement with the given options:
1. If the two lines intersect, then the two lines are not parallel.
2. If the two lines are not parallel, then the two lines intersect.
3. If the two lines do not intersect, then the two lines are parallel.
4. If the two lines are parallel, then the two lines do not intersect.
The correct inverse statement is:
"If the two lines do not intersect, then the two lines are parallel."
Therefore, the correct answer is:
OIf the two lines do not intersect, then the two lines are parallel.
