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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

Reflexive

AB = AB

Symmetric

If AB = CD, then CD = AB.

Transitive

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.

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