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What is the inverse of the following statement?

"If the corresponding angles are congruent, then the lines are parallel."

A. If the corresponding angles are not congruent, then the lines are not parallel.
B. If the lines are parallel, then the corresponding angles are congruent.
C. If the lines are not parallel, then the corresponding angles are not congruent.
D. If the corresponding angles are congruent, then the lines must be parallel.

Sagot :

GinnyAnsweridn
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."
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