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Warm Up
Write a conditional statement from each of the
following.
1. The intersection of two lines is a point.
If two lines intersect, then they intersect in a point.
2. An odd number is one more than a multiple of 2.
If a number is odd, then it is one more than a multiple of 2.
3. Write the converse of the conditional “If Pedro lives in
Chicago, then he lives in Illinois.” Find its truth value.
If Pedro lives in Illinois, then he lives in Chicago.
False: Counterexample- he could live in
Springfield, Illinois or any other city in the
state.
Definitions
Lesson 2.3
Objectives
 Students
will recognize and use
definitions.
 Students will recognize and use
biconditional statements.
What
is
a
Flopper?
Page 99 of your textbook
A flopper is a figure with one “eye” and
two “tails”.
Yes:
Flopper
No:
Only one tail
No :
has two eyes
Yes:
Flopper
Definition
 Biconditional
When a conditional statement and the
converse are both true
Conditional:
If a figure is a flopper, then it has one eye
and two tails
Converse:
If a figure has one eye and two tails, then it is
a flopper
Both the conditional and converse are true
Biconditional
“if and only if”
A statement that contains the phrase “if and only if”.
Writing a biconditional statement is equivalent to
writing a conditional statement and its converse.
Example:
If a figure is a flopper, then it has one eye and two tails
Converse:
If a figure has one eye and two tails, then it is a flopper
Both the conditional and converse are true
Biconditional statement:
A figure is a flopper if and only if it has one eye and two tails
Example:
If a person is between the ages of 13 to 19, then they are
a teenager.
Converse:
If a person is a teenager, then they are between the ages
of 13 and 19.
Both statements are true, so
both statements can be stated as One
Biconditional
A person is a teenager if and only if they are between the
ages of 13 and 19.
Biconditional

Also known as “if and only if”
If p and q are defined as the following:
p = is a teenager
q = a person between the ages of 13 and 19
The statement can be stated as:

p if and only if q

p iff q

In symbolic form:
pq
Biconditional Statements
 A biconditional
statement can either be
true or false.
 To be true both the conditional statement
and its converse must be true.
 All definitions can be written as true
biconditional statements.
A definition is a statement that describes a mathematical
object and can be written as a true biconditional.
Example: Writing Definitions as
Biconditional Statements
Write each definition as a biconditional.
A. A pentagon is a five-sided polygon.
A figure is a pentagon if and only if it is a 5-sided
polygon.
B. A right angle measures 90°.
An angle is a right angle if and only if it measures 90°.
Definition
 Adjacent
angles are angles in a plane that
have their vertex and one side in common
but no interior points in common.
Two angles are adjacent if and
only if they share a vertex and
one side.
Definition
Square is a quadrilateral with equal side
lengths and four 90 degree angles.
Stated as a bi-conditional:
A figure is a square if and only if the figure
has 4 sides of the same length and four 90
degree angles.
Assignment
#8 – 30
Due Thursday Oct 21
 P103
Read the directions carefully
#8-16 have four parts per problem
QUIZ on THURSDAY Oct 21