Question
Payton is working on a proof that consecutive interior angles are supplementary. Given that n ∥ m , fill in the following 2 column proof.(2 points)
Answers
GPT-4o mini
To prove that consecutive interior angles are supplementary given that line \( n \) is parallel to line \( m \), we can use a two-column proof format:
| **Statements** | **Reasons** |
|-------------------------------------------|---------------------------------------|
| 1. Lines \( n \) and \( m \) are parallel | 1. Given |
| 2. A transversal intersects lines \( n \) and \( m \) | 2. Definition of transversal |
| 3. Let angles \( A \) and \( B \) be consecutive interior angles on the same side of the transversal | 3. Definition of consecutive interior angles |
| 4. Angles \( A \) and \( B \) are interior angles formed by the transversal | 4. Properties of transversals |
| 5. By the Alternate Interior Angles Theorem, the angles formed are equal to each other | 5. Alternate Interior Angles Theorem |
| 6. Therefore, \( m \angle A + m \angle B = 180^\circ \) | 6. If two angles are supplementary, each angle is equal to \( 180^\circ \) |
| 7. Angles \( A \) and \( B \) are supplementary | 7. Definition of supplementary angles |
This proof demonstrates that consecutive interior angles are indeed supplementary when two lines are parallel and a transversal intersects them. If you need further elaboration or adjustments, feel free to ask!
| **Statements** | **Reasons** |
|-------------------------------------------|---------------------------------------|
| 1. Lines \( n \) and \( m \) are parallel | 1. Given |
| 2. A transversal intersects lines \( n \) and \( m \) | 2. Definition of transversal |
| 3. Let angles \( A \) and \( B \) be consecutive interior angles on the same side of the transversal | 3. Definition of consecutive interior angles |
| 4. Angles \( A \) and \( B \) are interior angles formed by the transversal | 4. Properties of transversals |
| 5. By the Alternate Interior Angles Theorem, the angles formed are equal to each other | 5. Alternate Interior Angles Theorem |
| 6. Therefore, \( m \angle A + m \angle B = 180^\circ \) | 6. If two angles are supplementary, each angle is equal to \( 180^\circ \) |
| 7. Angles \( A \) and \( B \) are supplementary | 7. Definition of supplementary angles |
This proof demonstrates that consecutive interior angles are indeed supplementary when two lines are parallel and a transversal intersects them. If you need further elaboration or adjustments, feel free to ask!