When a conditional statement and its converse are both true, you can write it as a single biconditional statement.
A point divides a segment into two congruent segments if and only if it is the midpoint of the segment
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 a point divides a segment
into two congruent segments,
then it is the midpoint of the segment.
By the definition of a midpoint, 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 a point is the midpoint of a segment,
then it divides the segment in
two congruent segments.
By the same definition, this is also true! Therefore, we can write the given statement as a biconditional statement.
Biconditional statement
A point divides a segment into
two congruent segmentsif and only if
it is the midpoint of the segment.
