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Answer :
Sure! Let's break down the problem step-by-step to find the correct answer.
### Original Statement and Converse
We begin with the original conditional statement:
- Original Statement: If a transversal passes through two parallel lines, then the consecutive interior angles formed between the parallel lines are supplementary.
### Understanding the Converse
The converse of a conditional statement is formed by swapping the hypothesis and the conclusion. So, for the statement "If P, then Q," the converse would be "If Q, then P."
Given:
- Original Statement: If P, then Q.
- P: A transversal passes through two parallel lines.
- Q: The consecutive interior angles formed between the parallel lines are supplementary.
To form the converse:
- Converse Statement: If Q, then P.
- Q: The consecutive interior angles formed between two lines cut by a transversal are supplementary.
- P: The two lines are parallel.
Therefore, the converse statement is:
- Converse Statement: If the consecutive interior angles formed between two lines cut by a transversal are supplementary, then the two lines are parallel.
### Choosing the Correct Answer
Among the given choices, we match the converse statement to find:
- Correct Answer: If the consecutive interior angles formed between two lines cut by a transversal are supplementary, then the two lines are parallel.
### Summary
So, the correct choice is:
- "If the consecutive interior angles formed between two lines cut by a transversal are supplementary, then the two lines are parallel."
### Original Statement and Converse
We begin with the original conditional statement:
- Original Statement: If a transversal passes through two parallel lines, then the consecutive interior angles formed between the parallel lines are supplementary.
### Understanding the Converse
The converse of a conditional statement is formed by swapping the hypothesis and the conclusion. So, for the statement "If P, then Q," the converse would be "If Q, then P."
Given:
- Original Statement: If P, then Q.
- P: A transversal passes through two parallel lines.
- Q: The consecutive interior angles formed between the parallel lines are supplementary.
To form the converse:
- Converse Statement: If Q, then P.
- Q: The consecutive interior angles formed between two lines cut by a transversal are supplementary.
- P: The two lines are parallel.
Therefore, the converse statement is:
- Converse Statement: If the consecutive interior angles formed between two lines cut by a transversal are supplementary, then the two lines are parallel.
### Choosing the Correct Answer
Among the given choices, we match the converse statement to find:
- Correct Answer: If the consecutive interior angles formed between two lines cut by a transversal are supplementary, then the two lines are parallel.
### Summary
So, the correct choice is:
- "If the consecutive interior angles formed between two lines cut by a transversal are supplementary, then the two lines are parallel."
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