# Postulate

Written by Jerry Ratzlaff on . 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.