When a conditional statement and its converse are both true, you can write it as a single biconditional statement.
An angle is a right angle if and only if its measure is 90^(∘).
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 statement.
Conditional statement
If an angle is a right angle,
then its measure is $90^(∘)$.
By the definition of a right angle, 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 an angle's measure is $90^(∘)$,
then it is a right angle.
This is also true! Therefore, we can write the given statement as a biconditional statement.
Biconditional statement
An angle is a right angle if and only if
its measure is $90^(∘)$.
