Section 2.4 – Building a System of Geometry Knowledge

Algebraic Properties of Equality

Let a, b, and c be real numbers or expressions representing real numbers.

Addition Property (add same to both sides) If a = b, then a + c = b + c

Subtraction Property (subtract same from both sides) If a = b, then a – c = b – c

Multiplication Property (multiply same to both sides) If a = b, then ac = bc

Division Property (divide same on both sides) If a = b, then

Substitution Property If a = b, you can plug b (or a) into the equation and it’s equal

Equivalence Property of Equality

Reflexive Property For any real number a, a = a

Symmetric Property For any real numbers a and b, if a = b, then b = a

Transitive Property For any real numbers a, b, and c, if a = b and b = c, then a = c