2.1.4 Biconditional Statements and Definitions

Key Objectives • Write and analyze biconditional statements. Key Terms • A biconditional statement is a statement that can be written in the form “ p if and only if q .” This means “if p then q ” and “if q then p .”

• A definition is a statement that describes an object and can be written as a true biconditional. • A polygon is a closed plane figure formed by three or more segments, where each segment intersects exactly two other segments only at their endpoints and no two segments with a common endpoint are collinear. • A triangle is a three-sided polygon. • A quadrilateral is a four-sided polygon. Example 1 Identifying the Conditionals within a Biconditional Statement

A biconditional statement can be thought of as a combination of two conditionals. The usual notation used for a biconditional statement is the double arrow. Sometimes a biconditional may be written using “iff” instead of the double arrow.

Remember, if a conditional relates two statements p and q where p is the conditional’s hypothesis and q is the conditional’s conclusion, then the converse of that conditional is the statement where q is the hypothesis and p is the conclusion. In other words, the converse of a conditional just switches the hypothesis and the conclusion. A conditional has a p statement and a q statement. To write a conditional and its converse from a biconditional, identify the p statement and the q statement in the biconditional. Then, write the conditional as “if p , then q ” and write the converse as “if q , then p .”

In this example, the p statement in the biconditional is “an angle is a right angle” and the q statement in the biconditional is “the angle measures 90°.”

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