Chapter 2 Overview Flashcards
inductive reasoning
reasoning based on patterns you observe
conjecture
conclusion you reach using inductive reasoning
counterexample
an example that shows a conjecture is incorrect
Conditional Statements
conditional → if-then statement
hypothesis → part p that follows if
conclusion → part q that follows then
(p → q ; read “If p, then q.”)
negation
opposite of the statement
symbol is ~ p and read “not p”
converse
(switch the
hypothesis &
conclusion)
If ∠ A is acute, then m ∠ A = 15.
(q → p)
inverse
(negate both
hypothesis &
conclusion)
If m ∠ A ≠ 15, then ∠ A is not acute.
~ p → ~ q
contrapositive
(negate both the
hypothesis & conclusion
of the converse)
If ∠ A is not acute, then m ∠ A ≠ 15.
~ q → ~ p
Equivalent Statements
have the same truth value
A conditional and its contrapositive are equivalent statements. They are
both true or both false.
The converse and inverse are also equivalent statements.
compound statement
combines 2 or more statements
conjunction
Connect two or more
statements with and.
s ⋀ j
You say “s and j.”
A conjunction is true only when both statements are true.
disjunction
Connect two or more
statements with or.
s ∨ j
You say “s or j.”
A disjunction is false only when both statements are false.
truth table
lists all possible combinations of truth values for 2 or more statements
biconditional
single true statement that combines a true conditional and its true converse
➢ uses the phrase “if and only if”
Biconditional Statement
Combines p → q and q → p as p ↔ q
( read “p if and only if q”)
deductive reasoning
process of reasoning logically from given statements or
facts to a conclusion
Law of Detachment
Law
If the hypothesis of a true conditional is true,
the conclusion is true.
If p → q is true and p is true,
then q is true.
Law of Syllogism
allows you to state a conclusion from two true conditional
statements when the conclusion of one statement is the hypothesis of the other
statement
Symbols
If p → q is true
And q → r is true,
Then p → r is true.
Theorem 2-1: Vertical Angles Theorem
Vertical Angles are congruent
Theorem 2-2: Congruent Supplement Theorem
If two angles are supplements of the same angle (or of congruent angles), then the two
angles are congruent.
Theorem 2-3 Congruent Complements Theorem:
If two angles are complements of the same angle (or of congruent angles), then the two
angles are congruent.
Theorem 2-4
All right angles are congruent.
Theorem 2-5
If two angles are congruent and supplementary, then each is a right angle.
