Question
If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Converse of the Corresponding Angles Postulate
Same-Side Interior Angles Theorem
Alternate Interior Angles Theorem
Converse of the Alternate Interior Angles Theorem
Converse of the Corresponding Angles Postulate
Same-Side Interior Angles Theorem
Alternate Interior Angles Theorem
Converse of the Alternate Interior Angles Theorem
Answers
GPT-4o mini
The statement "If two parallel lines are cut by a transversal, then the alternate interior angles are congruent" is known as the **Alternate Interior Angles Theorem**.
Here's a brief explanation of the other terms mentioned:
- **Converse of the Corresponding Angles Postulate**: If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
- **Same-Side Interior Angles Theorem**: If two parallel lines are cut by a transversal, then the same-side interior angles are supplementary (add up to 180 degrees).
- **Converse of the Alternate Interior Angles Theorem**: If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
So, to summarize, the original statement describes the **Alternate Interior Angles Theorem**.
Here's a brief explanation of the other terms mentioned:
- **Converse of the Corresponding Angles Postulate**: If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
- **Same-Side Interior Angles Theorem**: If two parallel lines are cut by a transversal, then the same-side interior angles are supplementary (add up to 180 degrees).
- **Converse of the Alternate Interior Angles Theorem**: If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
So, to summarize, the original statement describes the **Alternate Interior Angles Theorem**.