Monday Wake Up

1. Tell me one thing you did over the weekend.

2. What is the difference between a paragraph proof and a column proof?

3. True or False:• If a quadrilateral is a square, then all

four sides are equal. • If all four sides of a quadrilateral are

equal, then the figure is a square.

1.7 Deductive Structure

Deductive structure: conclusions are justified by means of previously assumed or provided statements.

Four Elements:

1.Undefined terms

2.Assumptions known as postulates

3.Definitions

4.Theorems and other conclusions

Postulate: an unproven assumption

Definition: states the meaning of a term, they are ALWAYS reversible!

Example stated:

1 If a point is the midpoint of a segment, then the point divides the segment into 2 congruent segments.

2 If a point divides a segment into 2 congruent segments, then the point is midpoint of the segment.

Conditional Statement:

P hypothesis: “If” part of the statement.

Q conclusion: “Then” part of the statement.LOGIC:

p q (read) “If p, then q.”

“p implies q.”

Converse:

Of p implies q is q implies p

p q q p

Theorem: math statement you can prove

Come with number

Can’t use T1 to prove T1

Theorems and postulates are not always reversible!

If 2 <“s are right <‘s, then they are congruent. True

Converse:

If 2 <‘s are congruent, then they are right <‘s. FALSE!

T or F? Conditional statement and converse.

If an animal is a dog, then it has four legs.

If an animal has four legs, then it is a dog.

False!

If a student receives a B on the test, then his/her grade is between 80 and 90.

State the converse and tell if it is T or F.

If the students grade is between 80 and 90, then the student receives a B on the test. True.