Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
2-3
Biconditional Statements
and Definitions
Holt Geometry
Warm Up
Warm Up
Lesson Presentation
Lesson Presentation
Lesson Quiz
Lesson Quiz
Holt McDougal
Geometry

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Warm Up
Write a conditional statement from each of the
following.
1.
The intersection of two lines is a point.
2.
An odd number 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 two lines intersect, then they intersect in a
point.
If a number is odd, then it is one more than a
multiple of 2.
If Pedro lives in Illinois, then he lives
in Chicago; False.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Write and analyze biconditional
statements.
Objective

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
biconditional statement
definition
polygon
triangle
quadrilateral
Vocabulary

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
When you combine a conditional statement and its
converse, you create a
biconditional statement
.
A
biconditional statement
is a statement that
can be written in the form “
p
if and only if
q
.” This
means “if
p
, then
q
” and “if
q
, then
p
.”

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
p
q
means
p
q
and
q
p
The biconditional “
p
if and only if
q
” can also be
written as “
p
iff
q
” or
p
q
.
Writing Math

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Write the conditional statement and converse
within the biconditional.
Example 1A: Identifying the Conditionals within a
Biconditional Statement
An angle is obtuse if and only if its measure is
greater than 90° and less than 180°.
Let
p
and
q
represent the following.
p
: An angle is obtuse.
q
: An angle’s measure is greater than 90° and
less than 180°.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Example 1A Continued
The two parts of the biconditional
p
q
are
p
q
and
q
p
.
Conditional:
If an
is obtuse,
then
its measure is
greater than 90° and less than 180°.
Converse:
If an angle's measure is greater
than 90° and less than 180°,
then
it is obtuse.

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