When a conditional statement and its converse are both true, you can write it as a single biconditional statement.
Two angles are vertical angles if and only if their sides form two pairs of opposite rays.
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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 vertical angles,
then their sides form two pairs of opposite rays.By the definition of vertical 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 sides form two pairs of opposite rays,
then their angles are vertical 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 vertical angles if and only if
their sides form two pairs of opposite rays.
