| A | B |
|---|
| Angle Measure Postulate-Unique Measure Assumption | every angle has a unique measure from 0 to 180 degrees |
| Angle Measure Postulate-Unique Angle Assumption | given any ray VA and any real number r between 0 and 180 there is a unique angle BVA in each half plane of line VA such that the measure of angle BVA equals 0 |
| Angle Measure Postulate-Zero Angle Assumption | if ray VA and ray VB are the same ray then the measure of angle AVB is 0 |
| Angle Measure Postulate-Straight Angle Assumption | if ray VA and ray VB are opposite rays then the measure on angle AVB is 180 |
| Angle Measure Postulate-Angle Addition Property | if ray VC(except for point V) is in the interior of angle AVB then mAVC+mCVB=mAVB |
| Linear Pair Theorem | if two angles form a linear pair then they are supplementary |
| Vertical Angles Theorem | if two angles are vertical angles then they have equal measures |
| Reflexive Property of Equality | for any real numbers a b and c a=a |
| Symmetric Property of Equality | for any real numbers a b and c if a=b then b=a |
| Transitive Property of Equality | for any real numbers a b and c if a=b and b=c then a=c |
| Addition Property of Equality | for any real numbers a b and c if a=b then a+c=b+c |
| Multiplication Property of Equality | for any real numbers a b and c if a=b then ac=bc |
| Transitive Property of Inequality | for any real numbers a b and c if a<b and b<c then a<c |
| Addition Property of Inequality | for any real numbers a b and c if a<b then a+c<b+c |
| Multiplication Property of Inequality | for any real numbers a b and c if a<b and c>0 then ac<bc or if a<b and c<0 then ac>bc |
| Equation to Inequality Property | for any real numbers a b and c if a and b are positive numbers and a+b=c then c>a and c>b |
| Substitution Property | for any real numbers a b and c if a=b then a may be substituted for b in any expression |
| Corresponding Angles Postulate part a | if two corresponding angles have the same measure then the lines are parallel |
| Corresponding Angles Postulate part b | if the lines are parallel then corresponding angles have the same measure |
| Parallel Lines and Slopes Theorem | two nonvertical lines are parallel if and only if they have the same slope |
| Transitivity of Parallelism Theorem | in a plane if line l is parallel to line m and line m is parallel to line n then line l is parallel to line n |
| Two Perpendiculars Theorem | if two coplanar lines l and m are each perpendicular to the same line then they are parallel to each other |
| Perpendicular to Parallels Theorem | in a plane if a line is perpendicular to one of two parallel lines then it is also perpendicular to the other |
| Perpendicular Lines and Slopes Theorem | two nonvertical lines are perpendicular if and only if the product of their slopes is -1 |
