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 the Linear Pair Postulate.
Conditional Statement
&If two angles form a linear pair
&then they are supplementary.
Next we will evaluate 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 supplementary
&then they form a linear pair.
The converse is not true. Not all supplementary angles form a linear pair. Let's look at a pair of angles where this is the case.
Therefore, we know that the converse of the Linear Pair Postulate is not true, which means we cannot write it as a biconditional statement.
