When a conditional statement and its converse are both true, you can write it as a single biconditional statement.
Two angles are supplementary angles if and only if the sum of their measures is 180^(∘).
Practice makes perfect
When a conditional statement and its converse are both true, it can be rewritten as a single biconditional statement. If p is the hypothesis and q the conclusion, the biconditional statement is written as p if and only if q. Let's first write the if-then form of our definition.
Conditional statement
If two angles are supplementary angles,
then the sum of their measures is $180^(∘)$.
By the definition of supplementary angles, we know that this statement is true. Now let's check the converse of the statement. The converse of a conditional statement, q→ p, exchanges the hypothesis and the conclusion of the conditional statement.
Converse
If the sum of two angle measures is $180^(∘)$,
then they are supplementary angles.
By the same definition, this is also true! Therefore, we can write the given statement as a biconditional statement.
Biconditional statement
Two angles are supplementary angles if and
only if the sum of their measures is $180^(∘).$
