Sections 2-3 & 2-4

The ________ and _________ properties of equality state that for all numbers a,b, and c: if a=b then a+c=b+c and a-c=b-c.

Addition Subtraction

Properties of Algebra can be used for proofs in __________.

Geometry

The __________ and _________ properties of equality state that for all numbers a,b, and c: if a=b then ac=bc and if c (doesn't equal) 0, then a/c=b/c.

Multiplication Division

_______ of _______ can be used for proofs in Geometry.

Properties Algebra

The ________ property of equality sates that for every number a: a=a.

Reflexive

Law of __________ If p -> q is a true _________ and p is true, then q is true.

detachment conditional

The transitive property of equality states that for all _______ a, b, and c: if ___ and ___ then ___.

numbers a=b b=c a=c

A formal, or two-column, proof lists a ________ for each step leading from the ________ to the _________ of a _________.

reason hypothesis conclusion conditional

The Substitution property of equality states that for all numbers a and b: if a=b then a may be ______ by b in any equation or expression.

replaced

The _______ property of equality states that for all numbers a,b, and c: if a=b and b=c then a=c.

transitive

Law of Syllogism If p -> q and q -> r are ___ conditionals, then ____ is also true.

true p -> r

Law of Detachment If p-> q is a ___ conditional and p is ___, then q is ____.

true true true

The ________ property of equality states that for all numbers a,b, and c: a(b+c)=ab+ac

Distributive

The reflexive property of equality states that for every _____ a: ____.

number a=a

The Distributive property of equality states that for all _______ a,b, and c: __________.

numbers a(b+c)=ab+ac

The Addition and Subtraction properties of equality state that for all _______ a,b, and c: if ___ then _____ and _____.

numbers a=b a+c=b+c a-c=b-c

The ________ property of equality states that for all numbers a and b: if a=b then a may be replaced by b in any equation or expression.

Substitution

Law of __________ If p -> q and q-> r are true _________, then p -> r is also true.

Syllogism conditionals

The _______ property of equality states that for all numbers a and b: if a=b then b=a.

Symmetric

The Substitution property of equality states that for all numbers a and b: if ___ then _ may be replaced by _ in any equation or expression.

a=b a b

A _____, or _________, proof lists a reason for each step leading from the hypothesis to the conclusion of a conditional.

formal two-column

The Multiplication and Division properties of equality state that for all _______ a,b, and c: if ___ then _____ and if ___, then _____.

numbers a=b ac=bc c (doesn't equal 0) a/c=b/c

The symmetric property of equality states that for all ______ a and b: if ___ then ___.

numbers a=b b=a