Proofs Involving Parallel Lines and Angles

The video tutorial explains the consecutive interior angles converse theorem, which states that if two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel. The tutorial sets up a two-column proof, using the given information that angles are supplementary and congruent. It concludes by proving the lines are parallel using the alternate interior angles converse theorem.

What does the consecutive interior angles converse theorem state?

• If two lines are cut by a transversal and the alternate interior angles are supplementary, the lines are parallel.

• If two lines are cut by a transversal and the consecutive interior angles are supplementary, the lines are parallel.

• If two lines are cut by a transversal and the consecutive interior angles are congruent, the lines are parallel.

• If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.

What is the given condition in the setup of the proof?

• Angle four and angle five are supplementary.

• Angle four and angle six are congruent.

• Angle three and angle five are supplementary.

• Angle three and angle six are congruent.

Which theorem is used as a strategy in the proof?

• Linear pair postulate

• Vertical angles theorem

• Corresponding angles postulate

• Alternate interior angles converse

Why are angles three and six considered congruent in the proof?

• They are both supplementary to angle five.

• They are both supplementary to angle four.

• They are both congruent to angle four.

• They are both congruent to angle five.

What is the reason for angles being congruent if they are supplementary to the same angle?

• They are corresponding angles.

• They are alternate interior angles.

• They form a linear pair.

• They are supplementary to the same angle.

What is the conclusion of the proof regarding lines l and m?

• Lines l and m are perpendicular.

• Lines l and m are skew.

• Lines l and m are parallel.

• Lines l and m are congruent.

What does the alternate interior angles converse state?

• If alternate interior angles are supplementary, the lines are perpendicular.

• If alternate interior angles are congruent, the lines are perpendicular.

• If alternate interior angles are congruent, the lines are parallel.

• If alternate interior angles are supplementary, the lines are parallel.

How does the proof use the alternate interior angles converse?

• To conclude that lines l and m are perpendicular.

• To show that angles four and six are supplementary.

• To conclude that lines l and m are parallel.

• To show that angles three and five are congruent.

What is the final step in the proof?

• Concluding that lines l and m are parallel.

• Stating that angle three and angle five are congruent.

• Stating that angle four and angle six are supplementary.

• Concluding that lines l and m are perpendicular.

What is the purpose of the proof discussed in the video?

• To prove the alternate interior angles converse theorem.

• To prove the consecutive interior angles converse theorem.

• To prove that all angles are supplementary.

• To prove that all angles are congruent.