Biconditional: 5
x
– 8 = 37 if and only if
x
= 9.
Biconditional: Two angles have the same measure if
and only if they are congruent.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Check It Out!
Example 2a
If the date is July 4th, then it is
Independence Day.
For the conditional, write the converse and a
biconditional statement.
Converse: If it is Independence Day, then the
date is July 4th.
Biconditional: It is July 4th if and only if it is
Independence Day.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Check It Out!
Example 2b
For the conditional, write the converse and a
biconditional statement.
If points lie on the same line, then they are
collinear.
Converse: If points are collinear, then they lie on
the same line.
Biconditional: Points lie on the same line if and
only if they are collinear.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
For a biconditional statement to be true,
both the conditional statement and its
converse must be true. If either the
conditional or the converse is false, then
the biconditional statement is false.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Determine if the biconditional is true. If false,
give a counterexample.
Example 3A: Analyzing the Truth Value of a Biconditional
Statement
A rectangle has side lengths of 12 cm and 25 cm
if and only if its area is 300 cm
2
.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Example 3A: Analyzing the Truth Value of a Biconditional
Statement
Conditional: If a rectangle has side
lengths of 12 cm and 25 cm, then its
area is 300 cm
2
.
Converse: If a rectangle’s area is
300 cm
2
, then it has side lengths of
12 cm and 25 cm.
The conditional
is true.
The converse
is false.
If a rectangle’s area is 300 cm
2
, it could have
side lengths of 10 cm and 30 cm. Because the
converse is false, the biconditional is false.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Determine if the biconditional is true. If false,
give a counterexample.
Example 3B: Analyzing the Truth Value of a Biconditional
Statement
A natural number
n
is odd
n
2
is odd.
Conditional: If a natural number
n
is odd, then
n
2
is odd.
The conditional is
true.
Converse: If the square
n
2
of a
natural number is odd, then
n
is odd.
The converse is true.
Since the conditional and its converse
are true, the biconditional is true.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Check It Out!
Example 3a
An angle is a right angle iff its measure is 90°.
Determine if the biconditional is true. If false,
give a counterexample.

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