Chapter 3 - Postulates and Theorems
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21 terms
Terms | Definitions |
|---|---|
 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 |
| Angle Addition Assumption | 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 |
| Addition Property of Equality | 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 |
| Addition Property of Inequality | a < b, then a + c < b + c |
| Multiplication Property of Inequality | if a < b, then a x c < b x c (if c > 0) if a < b, then a x c > b x c (if c < 0) |
| Substitution Property of Equality and Inequality | if a = b, then a may be substituted for b |
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