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Adjacent Angles are a pair of angles with a common vertex and a common side, but no common interior points Angle bisector a ray that divides an angle into two adjacent angles that are congruent Angle Addition assumption If angles AVC and CVB are adjacent angles, then m<AVC + m<CVB= m<AVB, part of the angle measure postulate Complementry Angles Two angles that add up to 90 degrees Supplementry Angles any two angles that add to 180 degrees Equal Angle Measures Theorem If two angles have the same measure, their complements/supplements have the same measure Linear Pair two adjacent angles whose noncommon sides are opposite rays Linear Pair Theorem if two angles form a linear pair, then they are supplementary Vertical Angles two nonstraight angles are verticle angles if and only if the union of thier sides is two lines Verticle angles theorem If two angles are verticle angles then their measures are equal. Reflexive Property of Equality a=a Symmetric Property of Equality if a=b, then b=a Transitive Property of Equality if a=b and b=c, then a=c Addition property of equality if a=b, then a+c=b+c Multiplication property of equality if a=b, then ac=bc Transitive property of Inequality If a > b and b > c, then a > c Addition property of Inequality If a>b then a+c>b+c Multiplication property of Inequality if a>b then ac>bc if c>0 If a>b then ac<bc if c<0 Equation to Inequality Property If a+b=c, then c>a and c>b Substitution Property If a=b, then a can be substituted for b in any equation or expression Definintion of Proof A proof of a conditional is a sequence of justified conclusions strating with the antecedent and ending with the consequent Corresponding angles postulate Two corresponding angles have the same measure if and only ofthe lines are parallel 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 l//m and m//n, then l//n. Arc a set of points on a circle between its end points A and B Major arc part of a circle that measures from 180 to 360 minor arc part of a circle that measures less than 180 Sk theorem 1: Parallel property Under a size change Sk, the line through any two preimage points is parallel to the line through their images. Sk theorem 2: Collinearity is preserved Under Sk, the images of collinear points are collinear. Sk theorem 3: Angle measure is preserved Under Sk, an angle an its image have the same measure. 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