Postulate 1: Ruler postulate- The points on a line can be paired with real numbers in such a way that any two points can have the coordinates 0 and 1. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of the coordinates.

Postulate 2: Segment Addition postulate- States that segment of lines can be added.

Postulate 3: Protractor postulate- On AB in a given plane chose any point O between A and B. Consider OA and OB all the rays that can be drawn from O on one side of AB. These rays can be paired with real numbers from 0 to 180 in such a way that (1) OA is paired with 0, and OB with 180 (2) If OP is paired with x and OQ with y, then POQ = |x-y|.

Postulate 4: Angle addition postulate- States that angles can be added.

Postulate 5: A line contains at least two points; a plane three noncollinear points; and space four points noncoplanar.

Postulate 6: Through any two points there is exactly one line.

Postulate 7: Through any three points there is exactly one plane, and through any three noncollinear points there is exactly one plane.

Postulate 8: If two points are in a plane, then the line that contains those two points is also in that plane.

Postulate 9: If two planes intersect, their intersection is a line.

Postulate 10: If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Postulate 11: If two lines are cut by a transversal, and the corresponding angles are congruent, the lines are parallel.

Postulate 12: SSS; if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Postulate 13: SAS; if two sides and the included angle of one triangle are congruent to the other triangles, then the triangles are congruent.

Postulate 14: ASA; If two angles and the included side of one triangle are congruent to the other triangles, then the two triangles are congruent.

Theorems:...