Unit 2: Deductive Reasoning Flashcards
Conditional Statement
an “if-then” statement, aka conditionals
ex: “if p, then q”
Converse
a conditional formed by interchanging the hypothesis and the conclusion
ex: statement “if p, then q”
converse “if q, then p”
Counterexample
an example that proves the hypothesis true but the conclusion false
- it only takes one counterexample to disprove a statement
Biconditional
when both the conditional AND its converse are true
- can be a definition
Addition, Subtraction, Multiplication, and Division Properties of Equality
ex: if a=b, then a+c = b+c
ex: if a=b, then a-c = b-c
ex: if a=b, then a x c = b x c
ex: if a=b & c doesn’t = 0, then a/c = b/c
Distributive and Substitution Properties of Equality
ex: 3 (12-4) = 3 (12) - 3 (4)
ex: if a=10, then 6a+2 = 6(10)+2
Transitive Property of Equality
if a=b and b=c, then a=c
Symmetric Property of Equality
if a=b, then b=a
Reflexive Property of Equality
aka “the Identity Property”
ex: 12.5 = 12.5
Midpoint Theorem
If M is the midpoint of line AB, then AM=0.5AB and MB=0.5AB
Angle Bisector Theorem
If ray BX is the bisector of angle ABC, then m<ABX=0.5<ABC and m<XBC=0.5<ABC
Linear Pair Postulate
If <AOC is a straight angle and B is any point not on line AC, then m<AOB+m<BOC=180
Vertical Angles Theorem
Vertical angles are congruent
Congruent Supplements Theorem
If 2 angles are supplements of congruent angles (or the same angle), then the 2 angles are congruent
Congruent Complements Theorem
If 2 angles are complements of congruent angles (or the same angle), then the 2 angles are congruent
