2.1 Inductive Reasoning and Conjecture
Inductive Reasoning – Reasoning that uses a number of specific
examples to arrive at a conclusion.
Conjecture – A concluding statement reached using inductive
reasoning.
Counterexample – An example to show that a conjecture is not
true.
2.2 Logic
Truth Value – The truth or falsity of a statement.
Negation – The opposite meaning of a statement.
Compound Statement – Two or more statements joined by the
word and or or.
Conjunction – A compound statement using the word and.
Disjunction – A compound statement using the word or.
Truth Table – A convenient method for organizing the truth
values of statements.
2.3 Conditional Statements
Conditional Statement – A statement that can be written in
if-then form.
2.4 Deductive Reasoning
Deductive Reasoning – An argument using facts, rules,
definitions, or properties to reach a logical conclusion.
2.5 Postulates and Paragraph Proofs
Postulate – A statement that is accepted as true without proof.
Also known as an axiom.
Proof – A logical argument in which each statement you make
is supported by a statement that is accepted as true.
Theorem – A statement or conjecture that has been proven.
Paragraph Proof – An informal proof that involves writing a
paragraph to explain why a conjecture for a given situation is
true.
2.6 Algebraic Proof
Algebraic Proof – A proof that is made up of a series of
algebraic statements.
Two-Column Proof – A formal proof that contains statements
and reasons organized in two columns.
Property
Segments
Angles
Reflexive
AB = AB
𝑚<1=𝑚<1
If 𝑚 < 1 = 𝑚 < 2,
Symmetric
If AB=CD,
then 𝑚 < 2 = 𝑚 < 1.
then CD=AB.
If 𝑚 < 1 = 𝑚 < 2
Transitive
If AB=CD and CD=EF,
and 𝑚 < 2 = 𝑚 = 3,
then AB=EF.
then 𝑚 < 1 = 𝑚 < 3
2.7 Proving Segment Relationships
2.8 Proving Angle Relationships