Transversals and Inequalitities..........................................................

(The Transvesal Postulate) If two parallel lines are cut by a transversal, then corresponding angles have equal measures.

(The Parallel Postulate and Theorem) Given a line and a point not on the line, there is exactly one line through the point that is parallel to the given line.

(The Parallel Postulate) Given a line and a point not on the line, there can be no more than one line through the point that is parallel to the given line.

(The Perpendicular Postulate 1) Given a line and a point not on the line, there can be no more than one line through the point that is perpendicular to the given line.

(The Perpendicular Postulate 2) In a plane, given a line and a point on the line, there is exactly one line through the point that is perpendicular to the given line.

(The Unique Line Postulate) If A and B are two points, then there is exactly one line that contains points A and B (or) Two points determine a line.

(The Unique Point Postulate) If AB is a ray, then there is a unique point P on ray AB such that AP equals any specified length.

(The Line Postulate) A line contains an infinite number of points.

(Whole Greater Than Part Postulate) If a + b = c then c > a and c > b (or) a <> b

(Trichotomy Postulate) If a and b are real numbers, then exactly one of the following statements must be true: a = b or a > b or a < b

(Transitive Postulate of Inequality) If a > b and b > c then a > c (or) a > b > c

(Addition Postulate of Inequality) If a > b then a + c > b + c