Properties of Equality

Properties of Equality

• For all real numbers a, b, and c

Reflexive property: a = a

Symmetric property: If a = b then b = a

Transitive property: If a = b and b = c then a = c



• The properties are in alphabetical order, and the

number of variables in each property are also in order

– RST123

Properties of Equality

• Each property of equality has an equivalent statement in geometry

Reflexive property: AB = AB

mA = mA

Symmetric property: If AB = CD then CD = AB

If mA = mB then mB = mA

Transitive property: If AB = CD and CD = EF then AB = EF

If mA = mB and mB = mC then mA = mC



• Congruence is also an equivalence relationship

Reflexive property: AB  AB

A  A

Symmetric property: If AB  CD then CD  AB

If A  B then B  A

Transitive property: If AB  CD and CD  EF then AB  EF

If A  B and B  C then A  C

Properties of Equality

• For all real numbers a, b, and c

– Addition property: If a = b then a + c = b + c

• Adding the same number

to both sides of an equation produces an equivalent equation

– Subtraction property: If a = b then a – c = b – c

• Subtracting the same number

from both sides of an equation produces an equivalent equation

– Multiplication property: If a = b then ac = bc

• Multiplying both sides

of an equation by the same number produces an equivalent equation

– Division property: If a = b then a  c = b  c

• Dividing both sides

of an equation by the same number produces an equivalent equation

– Substitution property:

• Replacing any expression in an equation

by an equivalent expression produces an equivalent equation