Deductive and Inductive Reasoning and Algebraic Proofs

All even numbers are divisible by 2
AND 28 is even
THEN 28 is divisible by 2

• Inductive

• Deductive

__________________________ uses specific observations and patterns of behavior to make generalizations.

• Deductive reasoning

• Inductive reasoning

__________________________ uses facts to draw conclusions.

• Deductive Reasoning

• Inductive Reasoning

What conclusion can be drawn from the following statements?
If Todd goes to the movies, then Sarah will go to the movies.  
If Chris goes to the movies, then Todd will go to the movies.

• If Chris goes to the movies, then Sarah will go to the movies.

• If Todd goes to the movies, then Chris will go to the movies.

• If Sarah goes to the movies, then Chris will go to the movies.

• If Chris goes to the movies, then Todd will go to the movies.

Label the proof appropriately.

f

e

d

c

b

a

Simplify

Subtraction

Substitution

Tags

G.CO.C

Label the proof appropriately.

j

i

h

g

f

e

d

c

b

a

Addition

Distributive

Substitution

Substitution

Subtraction

Tags

G.CO.C

Put the reasons in order for the proof

a

b

c

given

Subtraction Property

Division Property

• transitive property

• reflexive property

• associative property

• symmetric property

What reason justifies statement #2?

• Definition of Midpoint

• Transitive Property

• Addition Property

• Segment Addition Postulate

• Substitution Property

Reasoning based on specific examples and patterns used to form conjectures is called ______________ reasoning.

• Inductive

• Deductive