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# Chapter 3 - Postulates and Theorems

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Unique Measure Assumption
every angle has a unique measure from 0 degrees to 180 degrees
Unique Angle Assumption
given a ray and any real number between 0 and 180 there is one unique angle
Straight Angle Assumption
if ray BA and ray BC are opposite rays then m<ABC = 180 degrees
Zero Angle Assumption
if ray XY and ray XZ are the same ray then m<XYZ = 0 degrees
If angles AVC and CVB are adjacent angles, then m<AVC + m<CVB = m<AVB
Corresponding Angles Postulate
a. If 2 corresponding angles have the same measure, then the lines are parallel
b. If 2 lines are parallel, then the corresponding angles have the same measure
Linear Pair Theorem
if 2 angles form a linear pair, then they are supplementary
Vertical Pair Theorem
if 2 angles are vertical angles, then they have equal measures
Parallel Lines and Slopes Theorem
2 non-vertical lines are parallel if and only if they have the same slope
Perpendicular Lines and Slopes Theorem
2 non-vertical lines are perpendicular if and only if the product of their slopes is -1
Reflexive Property
a = a
Symmetric Property
if a = b, then b = a
Transitive Property
if a = b and b = c, then a = c
a = b, then a + c = b + c
Subtraction Property of Equality
a = b, then a - c = b - c
Multiplication Property
if a = b, then a x c = b x c
Division Property of Equality
if a = b, then a/c = b/c
Transitive Property of Inequality
if a < b and b < c, then a < c