Postulate 1: Ruler Postulate
points on a line can be matched with real numbers.
Postulate 2: Segment Addition Postulate
if b is between a and c, then ab + bc = ac.
Postulate 3: Protractor Postulate
the measure of any angle is equal to the absolute value of the difference between the real numbers for oa and ob.
Postulate 4: Angle Addition Postulate
if P is in the interior of RST, then the measurement of RST is equal to the sum of the measures of RSP and PST.
Postulate 5: Two Points Postulate
Through any two points there is exactly one line.
Postulate 6: How many points in a line?
A line contains at least two points
Postulate 7: Intersecting Lines
If two lines intersect, then their intersection is exactly one point.
Postulate 8: 3 noncollinear Points
Through any three noncollinear points there exists exactly one plane
Postulate 9: Intersecting Planes
If two planes intersect, then their intersection is a line
Postulate 10: 2 points lie in a plane - what about the line containing them?
If two points lie in a plane, then the line containing them lies in the same plane
Postulate 11: Intersecting Planes
If 2 planes intersect, then their intersection is a line.
Theorem 2.1: Segment Congruence
Reflexive, Symmetric, Transitive
AB = AB
If AB = CD, then CD = AB.
If AB = CD and CD = EF, then AB = EF.
Theorem 2.3: Right Angles
All right angles are congruent.
Theorem 2.4: Supplementary Angles - congruent?
If 2 angles are supplementary to the same angle (or to congruent angles) then they are congruent.
Theorem 2.5: Complementary Angles - congruent?
If 2 angles are complementary to the same angle (or to congruent angles) then they are congruent.
Postulate 12: Linear Pairs
If two angles form a linear pair, then they are supplementary.
Theorem 2.6: Vertical Angles
Vertical angles are congruent.
Postulate 13: Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.
Postulate 14: Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Postulate 15: Corresponding angles
corresponding angles are congruent
Theorem 3.1: Alternate angles
alternate interior and exterior angles are congruent
Theorem 3.3: Consecutive Interior Angles
consecutive interior angles are supplementary
Postulate 16: Corresponding Angles Converse
if 2 lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.
Theorem 3.4: Alternate Interior/Exterior angles converse
If the alternate interior and exterior angles are congruent, the lines are parallel.
Theorem 3.6: Consecutive Interior Angles Converse
If the consecutive interior angles are supplementary, the lines are parallel.