Properties, Proofs

Conditional Statement

If p then q

Negation

The opposite of what the conditional statement is, not P

Inverse

Negate both they hypo. and conc. if not P then not Q

Converse

Exchange the hypo and the conc. If q, then P

Contrapositive

If not q then not P write the converse then negate the hyp. and conc.

Biconditional Stament

P if and only Q, write a conditional statement and its converse is true

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 axc=bxc

Division Property of Equality

if a=b, then a/c=b/c

Substitution Property

if a=b, they can replace each other in any equation or expression

Reflexive Property

a=a

Symmetric Property

If a=b, then b=a

Transitive Property

If a=b, and b=c, then a=c

Definiton of a right angle

<A is congruent to m<B ←→m<A=m<B

Definition of supplemntary angle

<A and <B ←→ m<A+m<B=180, are supplementary

Def. of complementary angles

If angle A and <B are comp←→m<A+m<B=90