Answer:
Segments are congruent if and only if they have the same length.
Segments have the same length if and only if they are congruent.
Step-by-step explanation:
Biconditional statement
A biconditional statement is a combination of a conditional statement and its converse. It is conditional in both directions:
- Hypothesis "if and only if" conclusion.
- Conclusion "if and only if" hypothesis.
Write the given statement as a conditional statement:
- If segments are congruent, then they have the same length.
Write the given statement as a converse of the conditional statement:
- If segments have the same length, then they are congruent.
Both the conditional and converse statements must have the same truth value to produce a biconditional statement. Therefore, as both are true, we can write the biconditional statements:
- Segments are congruent if and only if they have the same length.
- Segments have the same length if and only if they are congruent.
