Question

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Rewrite the following definition of congruent segments as a biconditional statement:

Congruent segments have the same length.

Answer 1

A segment is congruent to another segment if and only if they have the same length.

Answer 2

Segments are congruent if and only if they have the same length.

Segments have the same length if and only if they are congruent.

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.