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 mÐa = mÐb, then mÐa + mÐc = mÐb + mÐc.

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

 

Subtraction Property of Equality                If mÐa = mÐb, then mÐa – mÐc = mÐb – mÐc.

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

 

Multiplication Property of Equality            If mÐa = mÐb, then mÐa * n = mÐb * n.

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

 

Division Property of Equality                      If mÐa = mÐb, then mÐa/n = mÐb/n.

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

 

Substitution Property of Equality               If mÐa = mÐb, then you may replace mÐb

with mÐa in any expression.

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

 

Transitive Property of Equality                   If mÐa = mÐb and mÐb = mÐc, then mÐa = mÐc.

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

 

Reflexive Property of Equality                    mÐa = mÐa;  AB = AB

 

Symmetric Property of Equality                  If mÐa = mÐb, then mÐb = mÐa.

                                                                        If AB = CD, then CD = AB.

 

 

GEOMETRIC PROPERTIES OF CONGRUENCE

 

Substitution Property of Congruence         If Ða @ Ðb, then you may replace Ðb

with Ða in any expression.

If AB @ CD, then you may replace CD

with AB in any expression.

 

Transitive Property of Congruence                        If Ða @ Ðb and Ðb @ Ðc, then Ða @ Ðc.

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

 

Reflexive Property of Congruence              Ða @ Ða;  AB @ BA

 

Symmetric Property of Congruence           If Ða @ Ðb, then Ðb @ Ða

If AB @ CD, then CD @ AB.