(1) Reflexive Property-- A quantity is congruent (equal) to itself. \(a=a\)
(2) Symmetric Property-- If \(a = b\), then \(b = a\).
(3) Transitive Property-- If \(a = b\) and \(b = c\), then \(a = c\).
(4) Addition Postulate-- If equal quantities are added to equal quantities, the sums are equal.
(5) Subtraction Postulate-- If equal quantities are subtracted from equal quantities, the differences are equal.
(6) Multiplication Postulate-- If equal quantities are multiplied by equal quantities, the products are equal. (also Doubles of equal quantities are equal.)
(7) Division Postulate-- If equal quantities are divided by equal nonzero quantities, the quotients are equal. (also Halves of equal quantities are equal.)
(8) Substitution Postulate-- A quantity may be substituted for its equal in any expression.
(9) Partition Postulate-- The whole is equal to the sum of its parts.
Also: Betweeness of Points: \(AB + BC = AC\).
Angle Addition Postulate: \(\angle ABC + \angle CBD = \angle ABD\).
(10) Construction-- Two points determine a straight line.
(11) Construction-- From a given point on (or not on) a line, one and only one perpendicular can be drawn to the line.