Parallel Line Proofs

If two angles are each equal to a third angle, then they are equal to each other.

If two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel.

Vertical angles are always equal.

If two parallel lines are cut by a transversal, then each pair of corresponding angles is equal.

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

Angles that are on opposite sides of the transversal and inside the two lines.

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is equal.

Angles that are on the same side of the transversal and inside the two lines.

If two parallel lines are cut by a transversal, then each pair of same-side interior angles is supplementary.

Lines in a plane that never meet and are always the same distance apart.