Math

• Conditional statement


  A statement that can be written in the form "If P then Q," where P and Q are sentences
• Conditional statement


  • If P then Q
• Truth table


  The visual study of shapes, sizes, patterns, and positions
• Undefined terms

  • Point
  • Line
  • Plane
• Point


  • Describes a location, has no size, represented by a dot
• Line


  • Has infinite length, no width or thickness, extends infinitely in two directions, represented by a straight line with two arrowheads
• Plane


  • Flat surface extending infinitely in all directions, has infinite length and width but no thickness, usually represented by a four-sided figure
• Defined terms

  • Collinear points
  • Non-collinear points
  • Coplanar points
  • Non-coplanar points
  • Line segment
  • Ray
  • Opposite ray
• Line segment


  Part of a line consisting of two endpoints and all the points in between
• Ray


  Portion of a line that has only one endpoint and extends infinitely in the other direction
• Opposite rays


  Rays with a common endpoint but extending in opposite directions
• Congruent triangles


  Triangles that have the same shape and size, with pairs of corresponding sides and angles being equal
• Triangle congruence postulates

  • Side-side-side (SSS)
  • Side-angle-side (SAS)
  • Angle-side-angle (ASA)
  • Angle-angle-side (AAS)
• Parallel lines


  Lines that do not intersect or meet each other at any point in a plane, equidistant at all points, and never converging or diverging
• Transversal lines


  Lines that intersect two or more lines at distinct points
• Undefined terms


  Terms that cannot be precisely defined, can only be described or illustrated
• Defined terms


  Terms that have a formal definition, used to define even more terms
• Axioms/Postulates


  Statements accepted as true without proof, can be used as reasons in proving mathematical statements
• Theorems


  Statements that can be proven, can also be used as reasons in proving other statements
• Geometry is the visual study of shapes, sizes, patterns, and positions, occurring in all cultures through at least one of the five strands of human activities: buildings/structures, machines/motion, navigating/star-gazing, arts/patterns, measurement
• Parts of a mathematical system

  • Undefined terms
  • Defined terms
  • Axioms/Postulates
  • Theorems
• Point


  Describes a location, has no size, represented by a dot
• Line


  Has infinite length, no width, nor thickness, extends infinitely in two opposite directions, represented by a straight line with two arrowheads
• Plane


  Flat surface extending infinitely in all directions, has infinite length and width but no thickness, usually represented by a four-sided figure
• Defined terms related to points

  • Collinear points
  • Non-collinear points
  • Coplanar points
  • Non-coplanar points
• Subsets of a line

  • Line segment
  • Ray
  • Opposite ray
• Line segment


  Part of a line consisting of two endpoints and all the points in between
• Ray


  Portion of a line that has only one endpoint and extends infinitely in the other direction
• Opposite rays


  Rays with a common endpoint but extending in opposite directions
• Axiomatic system


  Set of axioms used to derive theorems
• Axiom


  Statement considered true and does not require proof, basic truth used to prove other statements
• For every theorem in math, there exists an axiomatic system that contains all the axioms needed to prove that theorem
• Postulates


  • Distance Postulate
  • Ruler Postulate
  • Ruler Placement Postulate
  • Line Postulate
  • Plane Postulate
  • Plane-Point Postulate
  • Plane-Line Postulate
  • Plane Intersection Postulate
• The Distance Postulate states that for every given pair of distinct points, there corresponds a unique positive real number which is the distance between the points
• The Ruler Postulate states that the points of a line can be placed in correspondence with real numbers such that every point corresponds to one real number, every real number corresponds to one point, and the distance between two points equals the absolute value of the difference of the corresponding numbers
• The Ruler Placement Postulate states that given any two points on a line, one point corresponds to 0 and the other to a positive real number
• The Line Postulate states that given any two distinct points, there is exactly one line containing both points
• The Plane Postulate states that any three points that do not lie on the same plane determine a plane
• The Plane-Point Postulate states that a plane contains at least three noncollinear points and a space contains at least four noncoplanar points
• The Plane-Line Postulate states that if two points lie in a plane, then the line containing them lies on the same plane