Download notes of conditional statements

1.7 Deductive Structure & 1.8 Statements of Logic
I. Structure of Geometry
Geometry is based on a deductive structure—a system of thought in which conclusions are justified by means
of
previously assumed or proved statements. Ever deductive structure contains the following four elements:
o Undefined terms (such as points and lines)
o Postulates—unproved assumption
o Not always reversible (meaning, its converse is not necessarily true)
o Definitions—states the meaning of a term or idea (such as acute angles, right angles)
o Are reversible (meaning, its converse is also true)
o Theorems—mathematical statement that can be proved
o Not always reversible (meaning, its converse is not necessarily true)
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Conditional Statements (Conditional)
If . . . , then . . . –Conditional statement.
Converse- interchange if and then
Inverse. . – negating the Conditional S.
Contrapositive. . – negating the Converse Statement.
If P then q
If q then p
If no p then not q
If not p then not q
If part = hypothesis = antecedent
Then = conclusion = consequence
If P then q is in the same as:
A)
B)
C)
D)
If P, q
q, if p
P implies q
P only if q
Venn Diagram
p
q
Ex) For the following Conditional, underline the hypothesis once and conclusion twice, write all 4
conditionals then state if each conditional is T or F
AB= BC, if B is the midpoint of AC