Postulates
Postulate 1 (Ruler Postulate)
1. The points on a line can be paired with the real numbers in such a way that any 2 points can have coordinates 0 and 1.
2. Once a coordinate systemhas been chosen in this way, the distance between any 2 points equals the absolute value of the difference of their coordinates.
Postulate 2 (Segment Addition Postulate) If B is between A and C, then AB+BC=AC.
Postulate 3 Protractor Postulate
Postulate 4 Angle Addition Postulate
Postulate 5 A line contains at least 2 points;a plan contains at least 3 points not all in 1 line; space contains at least 4 points not all in 1 plane.
Postulate 6 Through any 2 points there is exactly one line.
Postulate 7 Through any 3 points there is exactly one plane, and through any 3 noncollinear points there is exactly one plane.
Postulate 8 If 2 points are in a plane, then the line that contains the points is in that plane.
Postulate 9 If 2 planes intersect, then their intersection is a line.
Postulate 10 If 2 // lines are cut by a transversal, then corresponding angles are congruent.
Postulate 11 If 2 lines are cut by a transversal and alternate interior angles are congruent, then the lines are //.
Postulate 12 (SSS Postulate) If 3 sides of 1 triangle are congruent to 3 sides of another triangle, then the triangles are congruent.
Postulate 13 (SAS Postualte) If 2 sides and the included angle of 1 triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.
Postulate 14 (ASA Postulate) If 2 angles and the included side of 1 triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent.
Postulate 15 (AA Similarity Postulate) If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 2 angles are similar.
