To find the inverse of a given conditional statement, we need to swap the hypothesis and the conclusion of the statement and then negate both parts.
The given statement is:
"If two lines do not intersect, then the two lines are parallel lines."
The inverse can be formed by swapping the hypothesis and conclusion and negating both individual parts:
1. Original hypothesis: "two lines do not intersect."
2. Original conclusion: "two lines are parallel lines."
Negate both parts:
1. Negated hypothesis: "two lines intersect."
2. Negated conclusion: "two lines are not parallel lines."
Now form the inverse statement:
"If the two lines intersect, then the two lines are not parallel lines."
However, we need to find the inverse form that directly corresponds to the negated statement given among the options:
O If the two lines are not parallel, then the two lines intersect.
We see that the statement "If the two lines are not parallel, then the two lines intersect." correctly negates and swaps the hypothesis and conclusion:
- Hypothesis negated: two lines are not parallel.
- Conclusion negated: two lines intersect.
Therefore, the inverse of the original statement is:
"If the two lines are not parallel, then the two lines intersect."
Thus, the correct option is:
O If the two lines are not parallel, then the two lines intersect.
So, the inverse of the given statement is accurately reflected in the first option. The correct response to the question is:
1. "If the two lines are not parallel, then the two lines intersect."
This corresponds to the option:
O If the two lines are not parallel, then the two lines intersect.
