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| the union of two rays or segments that have the same endpoint |
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| two nonstraight and nonzero angles with a common side interior to the angle formed by the noncommon sides |
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| the ray in the interior of an angle that divides the angle into two angles of equal measure |
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| two angles with measures that sum to 90 degrees |
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| two angles with measures that sum to 180 degrees |
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| two adjacent angles are a linear pair if and only if their noncommon sides are opposite rays. |
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| two nonstraight angles are vertical angles if and only if the union of their sides is two lines |
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| a sequence of justified conclusions, leading from what is given or known to a final conclusion |
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| a correspondence between two sets of points such that each point in the preimage set has exactly one image and each point in the image set has exactly one preimage |
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| two segments, rays, or lines such that the lines containing them form a 90˚ angle |
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| a line, ray, or segment that intersects a segment at its midpoint but does not contain the segment |
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| In a plane, the line that bisects and is perpendicular to the segment. |
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| Reflexive Property of Equality |
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| Symmetric Property of Equality |
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| Transitive Property of Equality |
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| If a=b and b=c, then a=c. |
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| Addition Property of Equality |
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| Multiplication Property of Equality |
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| Transitive Property of Inequality |
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| If a is less than b and b is less than c, then a is less than c. |
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| Addition Property of Inequality |
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| If a is less than b then a + c is less than b + c. |
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| Multiplication Property of Inequality |
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| If a is less than b and c is positive, then ac is less than bc. If a is less than b and c is negative, then ac is greater than bc. |
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| Equation of Inequality Property |
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| If a + b = c then a is less than c and b is less than c. |
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| If a = b, then b can be substituted in for a in any expression. |
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| If two angles form a linear pair, then they are supplementary. |
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| If two angles are vertical angles then their measures are equal. |
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| Corresponding Angles Postulate |
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| Two corresponding angles have the same measure if and only if the lines are parallel. |
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| a part of a circle with a measure less than 180 degrees |
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| a part of a circle with a measure between 180 and 360 degrees |
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| an arc with a measure of 180 degrees |
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| an angle with its vertex at the center of a circle |
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| figure after a transformation with labels A'B'C' |
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| degree of rotation that is positive if it goes counterclockwise and negative if it goes clockwise |
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| If two angles are adjacent then the two angles add to give you the whole outside angle. |
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| any line that cuts at least two other lines |
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| parallel lines and slopes theorem |
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| two nonvertical lines are parallel if and only if they have the same slope |
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| transitivity of parallelism theorem |
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| If l is parallel to m and m is parallel to n, then l is parallel to n. |
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| Under a size change the new lines are parallel to the original lines, points that were collinear remain collinear, and angle measures do not change size. |
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| Two Perpendiculars Theorem |
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| If two coplanar lines l and m are each perpendicular to the same line, then they are parallel to each other. |
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| Perpendicular to Parallels Theorem |
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| In a plane, if a line is perpendicular to on of two parallel lines, then it is also perpendicular to the other. |
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| Perpendicular Lines and Slopes Theorem |
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| Two nonvertical lines are perpendicular if and only if the product of their slopes is -1 (aka opposite reciprocals) |
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