Proving Lines Parallel: Key Concepts and Techniques

What is the basic definition of parallel lines?

• Lines that intersect at one point

• Lines that are in the same plane and do not intersect

• Lines that are perpendicular to each other

• Lines that are in different planes

What is a transversal?

• A line that intersects only one line

• A line that intersects two or more lines at different points

• A line that is parallel to another line

• A line that is perpendicular to another line

If corresponding angles are congruent, what can be concluded about the lines?

• The lines are perpendicular

• The lines are parallel

• The lines are skew

• The lines intersect at one point

Which of the following is true about corresponding angles and parallel lines?

• If the corresponding angles are not congruent, the lines are parallel

• If the lines are parallel, the corresponding angles are congruent

• If the corresponding angles are congruent, the lines are not parallel

• If the lines are parallel, the corresponding angles are not congruent

What are alternate interior angles?

• Angles on opposite sides of the transversal and inside the parallel lines

• Angles on the same side of the transversal and outside the parallel lines

• Angles on opposite sides of the transversal and outside the parallel lines

• Angles on the same side of the transversal and inside the parallel lines

If alternate exterior angles are congruent, what can be concluded about the lines?

• The lines are skew

• The lines are perpendicular

• The lines intersect at one point

• The lines are parallel

What is the relationship between same side exterior angles when the lines are parallel?

• They are congruent

• They are supplementary

• They are complementary

• They are equal

What is the relationship between same side interior angles when the lines are parallel?

• They are congruent

• They are supplementary

• They are equal

• They are complementary

What is the first step in proving the alternate exterior angles theorem?

• Assume the lines are not parallel

• Draw the diagram

• Identify the corresponding angles

• Identify the vertical angles

What property is used to conclude that if one angle is congruent to a second, and the second is congruent to a third, then the first is congruent to the third?

• Symmetric Property

• Substitution Property

• Reflexive Property

• Transitive Property