Postulates and Theorems

• Line postulate - two points determine exactly one line.
• Plane postulate - three noncollinear points determine a plane.
• Plane intersection postulate - if two distinct planes intersect, then their intersection is a line.
• Flat line postulate - if two points are in a plane, then the line containing the points is in the same plane.
• Ruler postulate - a set of real numbers such that the distance between any two points of the line is the absolute value of the difference between the corresponding numbers.
• Segment addition postulate - the definition of betweenness
• Angle addition postulate - if D lies in the interior of angle ABC, then the measure of angle ABC is equal to the measure of angle ABD + the measure of angle CBD.
• Linear pair postulate - the angles in a linear pair are supplementary.
• Alternate interior angle postulate - if two parallel lines are cut by a transversal, then any pair of alternate interior angles are congruent.
• Alternate exterior angle theorem - if two parallel lines are cut by a transversal, then any pair of alternate exterior angles are congruent.
• Corresponding angle theorem - if two parallel lines are cut by a transversal, then the corresponding angles are congruent.
• Same side interior angle theorem - if two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary.
• Same side exterior angle theorem - if two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary.
• Corresponding Parts of Congruent Triangles are Congruent - meaning of CPCTC
• CPCTC - states that when two or more triangles are congruent then their corresponding sides and angles are also congruent or equal in measurements.