Reasoning in Algebra

Chapter 2 Section 4Reasoning in AlgebraProperties of EqualityAddition Property of EqualityIf , then.Example: ADD 5 to both sides!

Subtraction Property of EqualityIf , then.Example: SUBTRACT 3 from both sides!

Properties of Equality (cont.)Multiplication Property of EqualityIf , thenExample: MULTIPLY both sides by 2!

Division Property of EqualityIf and , then

Example:DIVIDE both sides 3!

Properties of Equality (cont.)Reflexive Property of EqualityA value is equal to itself

Symmetric Property of EqualityIf , then Example: If , then

Transitive Property of EqualityIf and , then

Properties of Equality (cont.)Substitution PropertyIf , then can replace in any expression. Example: If then 2 can replace in an expression such as

Distributive Property

You can justify each statement with a postulate, property, or definition.

Solve for , justify each step.Given:

AOCB

Angle Addition PostulateSubstitutionSimplifySubtraction Property of EqualityDivision Property of Equality

KNML

StatementsReasons

GivenDefinition of bisectSubstitutionSubtraction Property of EqualityDivision Property of EqualitySymmetric Property of Equality

We can use Segment Addition Postulate to justify statements about segment lengthsACB

Solve for y, justify each step.

Given: AC=21StatementsReasons

Segment Addition PostulateSubstitutionSimplifyAddition Property of EqualityDivision Property of Equality

Properties of CongruenceReflexive Property of CongruenceBADC

ABRVUTS

Properties of CongruenceSymmetric Property of Congruence

Transitive Property of Congruence

Name the property of Equality or Congruence that justifies each statement ________________________

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Reflexive property of Congruence

Addition property of Equality

Transitive property of Congruence

Symmetric property of Equality