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### 54 Cards in this Set

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 Line Intersection Theorem Two different lines intersect in at most one point. Linear Pair Theorem If two angles form a linear pair, then they are supplementary. Vertical Angle Theorem If two angles are verticla angles, then they have equal measures. Paralell Lines and Slopes Theorem Two nonvertical lines are parallel if and only if they have the same slope. Two Perpendiculars Theorem In a plane, if l is perpendicular to n and m is perpendicular to n, the l is perpendicular to n. 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. Unique Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Throught any tow points, there is exactly one line. Number Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Every line is a set of points that can be pit into a one-to-one correspindence with the real numbers, with any point on it cxorresponfing to 0 and any other point corresponding to 1. Dimension Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) (1) Given a line in a plane , there is at least on point in the plane thar s not on the line. (2) Given a plane in space. there is at least on point in space that is not in the plane. Flat Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) If two points lie in a plane, the line containing tem lies in the plane. Unique Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Through two noncollinear points, there is exactly one point. Intersecting Planes Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) If two different planes have a point in common, then their intersection is a line. Uniqueness Property (Distance Postulate; Some Postylates for Arthmetic and Geometry) On a line, there is a unigue distance between two points. Distance Formula (Distance Postulate; Some Postylates for Arthmetic and Geometry) If the two points on a line have coordinates x and y, the distance between them is |x-y|. Additive Property (Distance Postulate; Some Postylates for Arthmetic and Geometry) If B is on line segment AC, then AB+BC=AC. Triangle Inequality Postulate (Some Postylates for Arthmetic and Geometry) The sum of the lengths og any two sides of a truangle is greater than the length of the third side. Unique Measure Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry) Every angle has a unique measure from 0 degress to 180 degress. Unique Angle Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry) Given any ray 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=r. Unique Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Throught any tow points, there is exactly one line. Number Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Every line is a set of points that can be pit into a one-to-one correspindence with the real numbers, with any point on it cxorresponfing to 0 and any other point corresponding to 1. Dimension Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) (1) Given a line in a plane , there is at least on point in the plane thar s not on the line. (2) Given a plane in space. there is at least on point in space that is not in the plane. Flat Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) If two points lie in a plane, the line containing tem lies in the plane. Unique Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Through two noncollinear points, there is exactly one point. Intersecting Planes Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) If two different planes have a point in common, then their intersection is a line. Uniqueness Property (Distance Postulate; Some Postylates for Arthmetic and Geometry) On a line, there is a unigue distance between two points. Distance Formula (Distance Postulate; Some Postylates for Arthmetic and Geometry) If the two points on a line have coordinates x and y, the distance between them is |x-y|. Additive Property (Distance Postulate; Some Postylates for Arthmetic and Geometry) If B is on line segment AC, then AB+BC=AC. Triangle Inequality Postulate (Some Postylates for Arthmetic and Geometry) The sum of the lengths og any two sides of a truangle is greater than the length of the third side. Unique Measure Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry) Every angle has a unique measure from 0 degress to 180 degress. Unique Angle Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry) Given any ray 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=r. Unique Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Throught any tow points, there is exactly one line. Number Line Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Every line is a set of points that can be pit into a one-to-one correspindence with the real numbers, with any point on it cxorresponfing to 0 and any other point corresponding to 1. Dimension Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) (1) Given a line in a plane , there is at least on point in the plane thar s not on the line. (2) Given a plane in space. there is at least on point in space that is not in the plane. Flat Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) If two points lie in a plane, the line containing tem lies in the plane. Unique Plane Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) Through two noncollinear points, there is exactly one point. Intersecting Planes Assumption (Postulates of Euclidean Geometry; Point-Line-Plane Postulates) If two different planes have a point in common, then their intersection is a line. Uniqueness Property (Distance Postulate; Some Postylates for Arthmetic and Geometry) On a line, there is a unigue distance between two points. Distance Formula (Distance Postulate; Some Postylates for Arthmetic and Geometry) If the two points on a line have coordinates x and y, the distance between them is |x-y|. Additive Property (Distance Postulate; Some Postylates for Arthmetic and Geometry) If B is on line segment AC, then AB+BC=AC. Triangle Inequality Postulate (Some Postylates for Arthmetic and Geometry) The sum of the lengths og any two sides of a truangle is greater than the length of the third side. Unique Measure Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry) Every angle has a unique measure from 0 degress to 180 degress. Unique Angle Assumption (Angle Measure Postulate; Some Postylates for Arthmetic and Geometry) Given any ray 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=r. Relflexive Property Of equality a=a Symetric Property of Equality IFf a=b, the b=a. Transitive Property of Equality If a=b and b=c, then a=c. Addition Property of Equality If a=b, the a+c=b+c. Multiplucation Property of Equality If a=b, the ac=bc. Transitive Property of Inequality If a is less than b and b is less than c, the a is less than c. Addition Property of Inequality If a is less than b, than a+b is less than b+c Multiplucation Property of Inequality If a is less than b and c is less than 0, then ac is less than bc. If a is less than b and c is greater than 0, then ac is greater than bc. Equation to Inequality Property If a and b are positive numbers and a+b=c, then c is greater than a and c is greater than b. Substituation Property If a=b, then a may be substituted for b in any expression. Corresponding Angles Postulate (a) If two corresponding angles have the same measure, then the lines are parallel. (b) If the lines are parallel, then corresponding angles have the same measure.