When a conditional statement and its converse are both true, you can write it as a single biconditional statement.
Two line segments have the same length if and only if they are congruent segments.
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 two line segments have the same length,
then they are congruent segments.By the definition of congruent segments, 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 line segments are congruent,
then they have the same length.
This is also true! Therefore, we can write the given statement as a biconditional statement.
Biconditional statement
Two line segments have the same length if and
only if they are congruent segments.
