Chapter 3 Honors Geometry

inductive reasoning

guess/conjecture; doesn’t prove its true

deductive reasoning

facts,postulates,definitions,theorems; proves its true

direct proof

given → logical steps → prove

indirect proof

assume negation of prove → contradiction → original statement must be true; proof contradicts

Reflexive

a=a (mirror; everything=itself)

Symmetric

if a=b then b=a (switch sides)

Transitive

if a=b and b=c, then a=c (chain)

Substitution

replace equals with equals (swap if equal)

Partition

part + part = whole

Segment partition

Segment is ≅ to the sum of all its parts (cut+add)

Angle partition

An angle is ≅ to the sum of all its parts (split + add)

Addition

if equals are added, sums are equal (add=still equal)

Segment addition

Odd ≅ segments → ≅ sums

Angle Addition

add ≅ <s → ≅ sums

Subtraction

If = subtracted, then differences are = (subtract = still equal)

Multiplication

equals x equals = equal (multiply both sides)

Doubles

doubles of doubles are equal (2x)

Division

equals ÷ nonzero equals = equal (divide both sides)

Halves

Halves of equals are equal (÷ by 2)

Squares

squares of equals are equal (squaring keeps equality)

Roots

Positive roots of equals are equal (√ keeps equality)

Generalization

Broad statement based on examples

Conjecture

an educated guess

Counterexample

one example that shows a conjecture is false

Proof

logical explanation that shows a statement is true

Given/Prove

what you start with/ what you must show

Two-column proof

Statements + Reasons

Postulate

a statement accepted as true without proof

Theorem

a statement thats been proved using postulates and logic

Equivalence Relation

both reflexive, symmetric, and transitive