Unit 2 Flashcards
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Inductive reasoning
reasoning that uses a number of examples to arrive at a conclusion
conjecture
educated guess that is derived from inductive reasoning
counterexample
an example that shows a conjecture is False
Negation
A negation of a statement has the opposite truth value
shows by -p
conditional statement
A statement that can be written in if-then form
ex: p—->q
includes hypothesis + conclusion
Inverse
formed by negating the hypothesis and conclusion
-p —-> -q
Converse
Formed by switching the hypothesis and conclusion
Symbolic form= if q ———-> p
Contrapositive
Formed by negating and switching the hypothesis and conclusion
symbolic form= -q —–> -p
Equivalent statements
When two statements are both true or false
Which statements are logically equivalent
conditional and contrapositive
Which statements are logically equivalent when false
converse and inverse
Bi-conditional statements
The Conjunction of a conditional and it’s converse
Symbolic form of a bi-conditional
p <—-> q
When can you write a bi-conditional statement
when conditional and converse are true
Deductive reasoning
Using
facts
definitions
properties
laws of logic
to form a conjecture
Law of Detachment
If the hypothesis is true, then the conclusion is true
Law of Syllogism
Allos you to drow a conclusion from 2 conditional statements in which the conclusion of the first statement is the hypothesis of the 2nd statement
p-q
q-r
p-r
Addition Property of = def.
if a=b, then a+c = b+c
Subtraction property of equality
if a=b, then a -c = b - c
Multiplication prop of equality
if a=b, then ac=bc
Division prop of equality
If a=b + is not 0, then a/c=b/c
Substitution prop of equality
If a=b then a may be replaced by b in any expression or equation
What is substitution useful for
for values
Reflexive prop
a=a
Symmetric prop
a=b then b=a
Transitive prop
a=b and b=c then a=c
What can be used as reasons for two-column proofs
definition
Postulates
Theorems
Properties
Reflexive property of congruence
for any segment AB, Segment AB= Segment AB
Defintion of Congruence
Segment AB= Segment CD, then AB=CD
Definition of a Midpoint
If M is the midpoint of AB, then AM=MB
Def. of Def. of Segment Bisector
If a segment is bisected, then the segment is cut into two equal parts
Def. of Complementary angles
Complementary <—-> Sum is 90 degrees
Def. of Supplementary angles
Supplementary <—-> Sum is 180
Def. of Perpendicular
Perpendicular lines form a right anle
=, congruence sign, or words
Defintion of congruence
both = and congruence
=, congruence sign, or words
Definition of Angle Bisector
both = and congruence
=, congruence sign, or words
Definition of Complementary angles
=
=, congruence sign, or words
Definition of SUpplementary angles
=
=, congruence sign, or words
Definition of Perpendicular
words
Definition of a Right Angle
A right angle= 90 degree
=, congruence sign, or words
Definition of Right angle
=
=, congruence sign, or words
Angle Addition Postulate
=
Vertical angles theorem
if two angles are vertical, they are congruent
=, congruence sign, or words
VAT
congruent sign
Complement Theorem
If two angles form a right angle, then they are complementary
Right Angle ——> Complementary
Supplement Theorem
If two angles form a linear pair, then they are supplementary
Linear Pair—-> Supplementary
Congruent Complements Theorem
If angle A is complementary to B and C is complementary to B then A=C
Congruent Supplements Theorem
If angle A is supplementary to B and C is supplementary to B, then A=C
=, congruence sign, or words
Complement Theorem
Words
=, congruence sign, or words
Congruent Complements theorem
congruence sign
=, congruence sign, or words
Supplement Theorem
words
=, congruence sign, or words
Congruent Supplements theorem
Congruence sign
