ALGEBRAIC PROPERTIES OF EQUALITY

 

Addition Property of Equality If a = b, then a + c = b + c.

 

Subtraction Property of Equality If a = b, then a c = b c.

 

Multiplication Property of Equality If a = b, then a * c = b * c.

 

Division Property of Equality If a = b, then a/c = b/c.

 

Substitution Property of Equality If a = b, then you may replace b with a in

any expression.

 

Transitive Property of Equality If a = b and b = c, then a = c.

 

Reflexive Property of Equality a = a

 

Symmetric Property of Equality If a = b, then b = a

 

 

BASIC PROPERTIES OF ADDITION AND MULTIPLICATION

 

Addition Multiplication

Commutative Property a + b = b + a ab = ba

 

Associative Property (a + b) + c = a + (b + c) (ab)c = a(bc)

 

Identity Property a + 0 = a; 0 + a = a a(1) = a; 1(a) = a

 

Property of Zero Property a + (-a) = 0 a(0) = 0

 

Distributive Property a(b + c) = ab + ac or (b + c)a = ab + ac

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GEOMETRIC PROPERTIES OF EQUALITY

 

Addition Property of Equality If ma = mb, then ma + mc = mb + mc.

If AB = CD, then AB + EF = CD + EF

 

Subtraction Property of Equality If ma = mb, then ma mc = mb mc.

If AB = CD, then AB EF = CD EF.

 

Multiplication Property of Equality If ma = mb, then ma * n = mb * n.

If AB = CD, then AB * n = CD * n.

 

Division Property of Equality If ma = mb, then ma/n = mb/n.

If AB = CD, then AB/n = CD/n.

 

Substitution Property of Equality If ma = mb, then you may replace mb

with ma in any expression.

If AB = CD, then you may replace CD with AB in any expression.

 

Transitive Property of Equality If ma = mb and mb = mc, then ma = mc.

If AB = CD and CD = EF, then AB = EF.

 

Reflexive Property of Equality ma = ma; AB = AB

 

Symmetric Property of Equality If ma = mb, then mb = ma.

If AB = CD, then CD = AB.

 

 

GEOMETRIC PROPERTIES OF CONGRUENCE

 

Substitution Property of Congruence If a @ b, then you may replace b

with a in any expression.

If AB @ CD, then you may replace CD

with AB in any expression.

 

Transitive Property of Congruence If a @ b and b @ c, then a @ c.

If AB @ CD and CD @ EF, then AB @ EF.

 

Reflexive Property of Congruence a @ a; AB @ BA

 

Symmetric Property of Congruence If a @ b, then b @ a

If AB @ CD, then CD @ AB.