Proving Parallel Lines With Two Column Proofs  Geometry, Practice Problems  Summary and Q&A
TL;DR
Different types of angles such as alternate interior, alternate exterior, corresponding, and same side interior angles can be used to prove whether two lines are parallel or not.
Questions & Answers
Q: What are alternate interior angles?
Alternate interior angles are congruent angles that are on alternate sides of a transversal line. They are located inside the parallel lines. If alternate interior angles are congruent, the lines are parallel.
Q: Can alternate exterior angles prove parallel lines?
Yes, alternate exterior angles are congruent angles that are on opposite sides of the transversal line but outside the parallel lines. If alternate exterior angles are congruent, the lines are parallel.
Q: How can corresponding angles be used to prove parallel lines?
Corresponding angles are congruent angles that are on the same side of the transversal line. If the corresponding angles are congruent, the lines are parallel.
Q: What are same side interior angles?
Same side interior angles are angles that are on the same side of the transversal line. If same side interior angles are supplementary, meaning they add up to 180 degrees, then the lines are parallel.
Summary & Key Takeaways

Alternate interior angles, such as angles 3 and 6, are congruent angles that are on alternate sides of a transversal line. If alternate interior angles are congruent, the two lines are parallel.

Alternate exterior angles, such as angles 1 and 8, are congruent angles that are on opposite sides of the transversal line but outside the parallel lines. If alternate exterior angles are congruent, the lines are parallel.

Corresponding angles, such as angles 2 and 6, are congruent angles that are on the same side of the transversal line. If corresponding angles are congruent, the lines are parallel.