Introduction
Consider two lines in a plane. They either have one point in common, or they have no common point.
Parallel Lines
The perpendicular distance between two parallel lines is the same at all points.
Transversal
If two parallel lines are cut by a transversal, the alternate angles are equal.
Corresponding Angles Axiom
If two parallel lines are cut by a transversal, then the corresponding angles are equal.
Alternate Angles Axiom
If two parallel lines are cut by a transversal, the alternate angles are equal.
Allied Angles Axiom
If two parallel lines are cut by a transversal, then the allied angles are supplementary.
Summary
If two parallel lines are cut by a transversal, the corresponding angles are equal.
