The Parallel Postulate

Postulate-Through a point not on a line there is exactly one parallel to the given line.

Angles Formed When Parallel Lines Are Cut by a Transversal.

Theorem- If two parallel lines are cut by a transversal, each pair of alternate interior angles are congruent.

Theorem- If two parallel lines cut by a transversal, then any pair of the angles formed are either congruent or supplementary.

Six Theorems About Parallel Lines

Theorem- If two lines are cut by a transversal, each pair of alternate exterior angles are congruent.

Theorem-If two parallel lines are cut by a transversal, each pair of corresponding angles are congruent.

Theorem- If two lines are cut by a transversal, each pair of interior angles on the same side are supplementary.

Theorem- If two lines are cut by a transversal, each pair of exterior angles on the same side are supplementary.

Theorem- In a plane, if a line is perpendicular to one of the two parallel lines, it is perpendicular to the other.

Theorem- if two lines are parallel to a third line, they are parallel to each other.