A biconditional statement is a statement that combines a conditional statement and its converse. A biconditional statement contains the phrase if and only if.

A definition can be written as a biconditional statement. Consider the definition of complementary angles. Two angles whose measures have a sum of $90^{\circ }$ are called complementary angles. The hypothesis $p$ and conclusion $q$ can be written as follows. After identifying the parts, the definition can be written as a single biconditional statement.

	Statement
Conditional $p\Rightarrow q$	If $\text{two angles are complementary},$ $\text{then }\text{their measures have a sum of }90^{\circ }.$
Converse $q\Rightarrow p$	If $\text{the measures of two angles have }$ $\text{a sum of }90^{\circ },$ then $\text{the angles are complementary}.$
Biconditional $p\iff q$	$\text{Two angles are complementary}$ if and only if $\text{their measures have a sum of }90^{\circ }.$

A biconditional statement is true if and only if the conditional and its converse have the same truth value. This can be explained using the truth table for a biconditional.

Biconditional Statement
$p$	$q$	$p\iff q$
T	T	T
T	F	F
F	T	F
F	F	T