When a conditional statement and its converse are both true, you can write it as a single biconditional statement.
Two angles are adjacent angles if and only if they share a common vertex and side but have no common interior points.
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 share a common vertex and side
but have no common interior points,
then they are adjacent angles.
By the definition of adjacent 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 two angles are adjacent angles,
then they share a common vertex and side
but have no common interior points.
By the same definition, this is also true! Therefore, we can write the given statement as a biconditional statement.
Biconditional statement
Two angles are adjacent angles if and only if
they share a common vertex and side
but have no common interior points.
