Download 1.7 Deductive Structure

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.