# Shared Flashcard Set

## Details

Geometry - Swanson
Postulates
26
Mathematics
Not Applicable
11/11/2004

Term
 Point-Line-Plane Postulate a. Unique line Assumption
Definition
 [image] 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
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
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
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 PostulateSuppose 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 PostulateA-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
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