# Proving Parallel Lines With Two Column Proofs - Geometry, Practice Problems | Summary and Q&A

85.9K views
December 23, 2017
by
The Organic Chemistry Tutor
Proving Parallel Lines With Two Column Proofs - Geometry, Practice Problems

## 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.

## Key Insights

• 🫥 Alternate interior angles can prove parallel lines.
• 🫥 Alternate exterior angles can also be used to prove parallel lines.
• 🔺 Corresponding angles are another type of angles that can show parallel lines.
• 🫥 Same side interior angles can determine whether lines are parallel or not.
• 🔺 The converse of alternate interior angles, alternate exterior angles, and corresponding angles can also be used to prove parallel lines.
• 🤬 The parallel lines symbol is represented by the symbol "||".
• 🤬 The perpendicular lines symbol is represented by the symbol "⊥".

## Transcript

in this lesson we're going to focus on proven parallel lines so let's say if we have two lines let's call this line a and line b and these two lines are cut by a transversal line which we'll call t for transversal and let's say this is angle 1 2 3 4 5 6 seven and eight now the first thing you need to know is that if angles three and six are congrue... Read More

### 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.