Download DAY 3 2.1 Conditional Statements

DAY 3
2.1 Conditional Statements
Logic Statement Graphic Organizer
Statement
Symbol
Words
Conditional Statement
pq
If p, then q.
Related Conditional
Symbol
Words
Converse
qp
If q, then p.
Inverse
~p  ~q
If not p, then not q.
Contrapositive
~q  ~p
If not q, then not p.
Statement
Symbol
Words
p if and only if q
or
q if and only if p
Biconditional statement
p ↔ q or q ↔ p
Common Abreviation
p iff q
or
q iff p
GOALS
Understand Biconditionals.
Recognize and use definitions.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
JUSTIFYING STATEMENTS
In math, deciding if a statement is true or
false demands that you can justify your
answers. “Just because”, or, “It looks like
it” are not sufficient.
Justification must come in the form of
Postulates, Definitions, or Theorems.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
EXAMPLE 1
D
A
Statement
D, X, and B are collinear.
X
Truth Value
TRUE
C
September 17, 2015
B
Reason
Definition of collinear
points.
GEOMETRY 2.1 CONDITIONAL STATEMENTS
EXAMPLE 2
Statement
A
AC  DB
Truth Value
D
X
B
TRUE
Reason
C
Definition of
Perpendicular lines
Def  lines
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
EXAMPLE 3
Statement
D
A
CXB is adjacent
to BXA
X
Truth Value
TRUE
B
Reason
C
Def. of adjacent angles
Def. of adj. s
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
EXAMPLE 4
A
D
X
B
Statement
CXD and BXA are
vertical angles.
Truth Value
TRUE
Reason
C
Def. vertical angles
Def. vert. s
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
EXAMPLE 5
Statement
DXA and CXB are
adjacent angles.
Truth Value
A
D
X
B
FALSE
Reason
C
September 17, 2015
There is not a common
side. (Or, they are
vertical angles.)
GEOMETRY 2.1 CONDITIONAL STATEMENTS
VERY IMPORTANT!
In doing proofs, you must be able to
justify every statement with a valid
reason. To be able to do this you must
know every definition, postulate and
theorem. Being able to look them up is no
substitute for memorization.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
YOUR TURN
D
A
E B
F
September 17, 2015
H
C
G
GEOMETRY 2.1 CONDITIONAL STATEMENTS
YOUR TURN
False (they are not collinear)
True (sides are opposite rays)
True (post. 8)
D
A
E B
H
C
F
G
False (no rt.  mark)
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
YOUR TURN
True (def.  lines)
False (they are supplementary)
E B
True (half of 180 is 90 -- a right )
September 17, 2015
D
A
H
C
F
G
GEOMETRY 2.1 CONDITIONAL STATEMENTS
REVIEW OF BICONDITIONALS
PQ
Biconditional:
P iff Q.
ALL definitions can be written as biconditional statements.
Example
Perpendicular Lines: Two lines that intersect to form a right angle.
n
Notation:
mn
m
September 17, 2015
Biconditional Statement:
Two lines intersect to form a
right angle if and only if they
are perpendicular line.
GEOMETRY 2.1 CONDITIONAL STATEMENTS
BICONDITIONAL
If a statement is a biconditional, it means we
can write it two ways: as a conditional and as
its converse.
Biconditional
A line is horizontal if and only if its slope is zero.
Conditional
If a line is horizontal, then its slope is zero.
Converse
If the slope of a line is zero, then the line is horizontal.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
DEFINITIONS
ALL definitions are biconditionals.
Example:
Definition of Congruent Angles
Two angles are congruent iff they have the same
measure.
Conditional: If two angles are congruent, then they have
the same measure.
Converse: If two angles have the same measure, then
they are congruent.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
TRY IT.
An angle is obtuse iff it measures between 90 and 180.
Write the biconditional as a conditional and its converse.
If an angle is obtuse, then it measures between 90 and
180.
If an angle measures between 90 and 180, then it is
obtuse.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
TRUTH VALUES OF BICONDITIONALS
A biconditional is TRUE if both the
conditional and the converse are true.
A biconditional is FALSE if either the
conditional or the converse is false, or
both are false.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
EXAMPLE
Biconditional
or False?
False!
x = 5 iff x2 = 25. True
Conditional
true or False?
If x = 5, then x2 = 25. True
Converse
False!or False?
If x2 = 25, then x = 5. True
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
YOUR TURN
Write the following biconditional statement as a
conditional statement and its converse.
Two segments are congruent if and only if they have the
same measure.
Answer
Conditional: If two segments are congruent, then they
have the same measure.
Converse: If two segments have the same measure, then
they are congruent.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
WHAT YOU CAN DO NOW:
Identify statements about drawings as true or false.
Recognize and write biconditionals.
Write a conditional and its converse from a biconditional.
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS
ASSIGNMENT
2.1 Day 3 Biconditionals and Truth Value Worksheet
September 17, 2015
GEOMETRY 2.1 CONDITIONAL STATEMENTS