Respuesta :
The inverse of the statement "If the alternate interior angles are congruent, then the lines are parallel" is option "O If the alternate interior angles are not congruent, then the lines are not parallel."
In mathematics, an inverse statement is the opposite of a given statement. It is created by negating the original statement and switching the order of the statements. In this case, the original statement is "If the alternate interior angles are congruent, then the lines are parallel." To create the inverse statement, we negate the original statement by saying "If the alternate interior angles are not congruent," and we switch the order of the statements by saying "then the lines are not parallel."
Alternate interior angles are angles that are located on opposite sides of the transversal line, and on the inside of the two lines being intersected. They are congruent when the two lines being intersected are parallel. Therefore, the original statement is saying that if the two lines being intersected are parallel, then the alternate interior angles are congruent. The inverse statement is the opposite of this, and it is saying that if the two lines being intersected are not parallel, then the alternate interior angles are not congruent.
In summary, the inverse statement of "If the alternate interior angles are congruent, then the lines are parallel" is "If the alternate interior angles are not congruent, then the lines are not parallel" which is option O in the multiple choice question.
The reason is that an inverse statement is the opposite of a given statement. It is created by negating the original statement and switching the order of the statements. In this case, the original statement is "If the alternate interior angles are congruent, then the lines are parallel." To create the inverse statement, we negate the original statement by saying "If the alternate interior angles are not congruent," and we switch the order of the statements by saying "then the lines are not parallel."
Alternate interior angles are angles that are located on opposite sides of the transversal line, and on the inside of the two lines being intersected. They are congruent when the two lines being intersected are parallel. Therefore, the original statement is saying that if the two lines being intersected are parallel, then the alternate interior angles are congruent. The inverse statement is the opposite of this, and it is saying that if the two lines being intersected are not parallel, then the alternate interior angles are not congruent.
In summary, the inverse statement of "If the alternate interior angles are congruent, then the lines are parallel" is "If the alternate interior angles are not congruent, then the lines are not parallel" which is option O in the multiple choice question.
The answer is "O If the alternate interior angles are not congruent, then the lines are not parallel."
Answer:
D) If the alternate interior angles are not congruent, then the lines are not parallel.
Step-by-step explanation:
Conditional statement
"If this happens, then that will happen."
- Hypothesis: The part after the "if".
- Conclusion: The part after the "then".
Given conditional statement:
- "If the alternate interior angles are congruent, then the lines are parallel."
Therefore:
- Hypothesis: The alternate interior angles are congruent
- Conclusion: The lines are parallel.
Inverse statement
The inverse of a conditional statement is formed by negating the hypothesis and the conclusion.
Therefore, the inverse of the given conditional statement is:
- "If the alternate interior angles are not congruent, then the lines are not parallel."
