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Details Title: Geometry - Swanson Description: Postulates Total Flash Cards: 26 Created: 11/11/2004 07:36:25	To study from this set of flash cards, or to create your own your own study flash cards, register HERE. If you are already a registered user, CLICK HERE.
Cards Term Point-Line-Plane Postulate a. Unique line Assumption Definition Through any two points, there is exactly one line. Term Point-Line-Plane Postulate b. Number line assumption Definition Every line is a set of points that can be put into a 1 to 1 correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1. Term Point-Line-Plane Postulate c. Dimension Assumption Definition 1. Given a line in a plane, there is at least 1 point in the plane that is not on the line. 2. Given a plane in space, there is at least one point in space that is not in the plane Term Point-Line-Plane Postulate d. Flat Plane Assumption Definition If two points lie in a plane, the line containing them lies in the plane Term Point-Line-Plane Postulate e. Unique Plane Assumption Definition Through three noncollinear points, there is exactly 1 plane. Term Point-Line-Plane Postulate f. Intersecting Plane Assumption Definition If two different planes have a point in common, then their intersection is a line. Term Distance Postulate a. Uniqueness Property Definition On a line, there is a unique distance between two points Term Distance Postulate b. Distance Formula Definition If the two points on a line have coordinates x and y, the distance between them is [x - y] Term Distance Postulate c. Additive Property Definition If B is on segment AC, then AB + BC = AC. Term Triangle Inequality Postulate Definition The sum of the lengths of any two sides of a triangle is greater than the length of the third side Term Angle Measure Postulate a. Unique Measure Assumption Definition Every angle has a unique measure from 0 to 180 Term Angle Measure Postulate b. Unique Angle Assumption Definition 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 = r. Term Angle Measure Postulate c. Zero Angle Assumption Definition If ray VA and ray VB are the same ray, then the measure of angle AVB = 0. Term Angle Measure Postulate d. Straight Angle Assumption Definition If VA and VB are opposite rays, then the measure of angle AVB = 180 Term Angle Measure Postulate e. Angle Addition Property Definition If ray VC (except for point V) is in the interior of angle AVB, then the measure of angle AVC + measure of angle CVB = the measure of angle AVB Term Postulates of Equality a. Reflexive Property of Equality b. Symmetric Property of Equality d. Transitive Property of Equality Definition a. a = a (dumb property) b. If a = b then b = a c. If a = b and b = c then a = c Term Point-Line-Plane Postulate a. Unique line Assumption Definition Through any two points, there is exactly one line. Term Addition Property of Equality Definition If a = b, then a + c = b + c Term Multiplication Property of Equality Definition If a = b, then ac = bc Term Postulate of Inequality Transitive Property of Inequality Definition If a is less than b and b is less than c, then a is less than c. Term Addition Property of Inequality Definition If a is less than b, then a + c is less than b + c. Term Multiplication Properties of Inequality Definition If a is less than b and c is greater than 0, then ac is less than ab If a is less than b and c is less than 0, then ac is greater than ab Term Postulate of Inequality Property Definition If a and b are postive numbers and a + b = c, then c is greater than a and c is greater than b. Term Substitution Property Definition If a = b, then a may be substituted for b in any expression. Term Corresponding Angles Postulate Suppose two coplanar lines are cut by a transversal Definition 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. Term Reflection Postulate A-B-C-D postulate Definition a. Angle measure is preserved. b. Betweenness is preserved c. Collinearity is preserved. d. Distance is preserved. e. 1 to 1 correspondence f. Orientation is reversed