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