Conditional: If an angle is a right
angle, then its measure is 90°.
The conditional is
true.
Converse: If the measure of an
angle is 90°, then it is a right
angle.
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 3b
y
= –5
y
2
= 25
Determine if the biconditional is true. If false,
give a counterexample.
Conditional: If
y
= –5, then
y
2
= 25.
The conditional is
true.
Converse: If
y
2
= 25, then
y
= –5.
The converse is false.
The converse is false when
y
= 5.
Thus, the biconditional is false.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
In geometry, biconditional statements are used to write
definitions
.
A
definition
is a statement that describes a
mathematical object and can be written as a true
biconditional.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
In the glossary, a
polygon
is defined as a closed
plane figure formed by three or more line
segments.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
A
triangle
is defined as a three-sided polygon,
and a
quadrilateral
is a four-sided polygon.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Think of definitions as being reversible.
Postulates, however are not necessarily true
when reversed.
Helpful Hint

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Write each definition as a biconditional.
Example 4: Writing Definitions as Biconditional
Statements
A. A pentagon is a five-sided polygon.
B. A right angle measures 90°.
A figure is a pentagon if and only if it is a 5-sided
polygon.
An angle is a right angle if and only if it measures 90°.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Check It Out!
Example 4
4a. A quadrilateral is a four-sided polygon.
4b. The measure of a straight angle is 180°.
Write each definition as a biconditional.
A figure is a quadrilateral if and only if it is a 4-
sided polygon.
An
is a straight
if and only if its measure is
180°.

Holt McDougal
Geometry
2-4
Biconditional Statements
and Definitions
Lesson Quiz
1.
For the conditional “If an angle is right, then its
measure is 90°,” write the converse and a
biconditional statement.
2.
Determine if the biconditional “Two angles are
complementary if and only if they are both
acute” is true. If false, give a counterexample.
False; possible answer: 30° and 40°
Converse: If an
measures 90°, then the
is right.
Biconditional: An
is right iff its measure is 90°.
3.
Write the definition “An acute triangle is a
triangle with three acute angles” as a
biconditional.
A triangle is acute iff it has 3 acute
s.

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