Proofs Flashcards
conditional statement
a statement that can be written in if-then from
Hypothesis
the phrase following if in a conditional statement
conclusion
the phrase following then in a conditional
converse
switch the hypothesis and conclusion
counter example
proves conditional wrong
Bi-conditional
a statement that is true and the converse is true also - if and only if
visual reasoning
translate descriptions into diagrams and/or pictures to better understand the situation
inductive reasoning
the process of observing the data, recognizing patterns, and making conclusions
conjecture
a conclusion base on inductive reasoning
deductive reasoning
the process of showing certain statements must follow logically from agreed among assumptions and proven facts
addition P.o.E. (subtraction)
If A = B then A + C = B + C
Multiplication P.o.E. (division)
If A = B then A x C = B x C
Substitution P.o.E.
If A = B then A can be substituted of B in any equation/expression
Reflexive Property
A=A
A congruent to A
Symmetric Property
A = B so B = A
Transitive Property
congruence A = B, B = C so A = C
Theorem
a statement Deductively proven to be true from definitions, postulate, and previously proven theorems
Postulate
an unprovable statement assumed true
proof
a series of justified conclusion leading from given info to a result
two column proof
a proof that consists of a list of conclusions and the justifications that are true
segment addition postulate (SAP)
if B is on AC then AB+BC=AC
Segment addition Postulate (AAP)
if D is inside /ABC then /ABD + /DBC = /ABC
linear pair theorem
If 2 angles from a linear pair then they are supplementary
vertical angles theorem
if 2 angles vertical angles they are congruent
corresponding angles postulate
if // the C.A. are congruent
alternate interior angles theorem
if // then A.I.A are congruent
alternate exterior angles theorem
if // then A.E.A are congruent
same side interior angles theorem
if // then S.S.I.A are supp.
same side exterior angles theorem
if // then S.S.E.A are supp.
corresponding angles converse postulate
If C.A. are congruent the lines are //
alternate interior angles converse theorem
If A.I.A are congruent the lines are //
alternate exterior angles converse theorem
If A.E.A are congruent the lines are //
same side interior angles converse theorem
If S.S.I.A are congruent the lines are supp.
