Postulate

Written by Jerry Ratzlaff. Posted in Algebra

 A postulate is a statement that is assumed true without proof.

 Let \(\;a\; \) , \(\;b\; \) and \(\;c\; \) be real numbers.

  • Reflexive Property - \(\;a = a\; \) (A quantity is congruent (equal) to itself.)
  • Symmetric Property - If \(\;a = b\; \), then \(\;b = a \)
  • Transitive Property - If \(\;a = b\; \) and \(\;b = c\; \) , then \(\;a = c \)
  • Addition Postulate - If \(\;a = b\; \) , then \(\;a + c = b + c\; \)
  • Subtraction Postulate - If \(\;a = b\; \) , then \(\;a - c = b - c\; \)
  • Multiplication Postulate - If \(\;a = b\; \) , then \(\;ac = bc\; \)
  • Division Postulate - If \(\;a = b\; \) and \(\;c \ne 0\; \) , then \(\; \frac {a}{c} = \frac {b}{c}\; \)
  • Substitution Postulate - If \(\;a = b\; \) , then \(\;a\; \) can be substituted for \(\;b\; \) in any expression.
  • Distributive Postulate - \(\;a \left (b + c \right ) = ab + ac\; \)
  • A straight line contains at least two points.
  • If two lines intersect, the intersection is only one point.
  • If two planes intersect, the intersection is only one line.
  • A plane must contain at least three noncollinear points.