# Conditional Statements

A statement written in the if-then form is a conditional statement.

$p\to q$ represents the conditional statement

“if $p$ then $q$ .”

Example 1:

If two angles are adjacent , then they have a common side.

The part of the statement following if is called the hypothesis , and the part following then is called the conclusion.

Example 2:

Identify the hypothesis and conclusion of the following statement.

A polygon is a pentagon, if it has five sides.

Hypothesis : The polygon has five sides.

Conclusion : It is a pentagon.

## Biconditional Statement

A biconditional statement is a combination of a conditional statement and its converse written in the  if and only if  form.

Two line segments are congruent if and only if they are of equal length.

It is a combination of two conditional statements, “if two line segments are congruent then they are of equal length” and “if two line segments are of equal length then they are congruent.”

A biconditional is true if and only if both the conditionals are true.

Biconditionals are represented by the symbol $↔$ or $⇔$ .

$p↔q$ means that $p\to q$ and $q\to p$ . That is, $p↔q=\left(p\to q\right)\wedge \left(q\to p\right)$ .

Example:

Write the two conditional statements associated with the biconditional statement below.

A rectangle is a square if and only if the adjacent sides are congruent.

The associated conditional statements are:

a) If the adjacent sides of a rectangle are congruent then it is a square.

b) If a rectangle is a square then the adjacent sides are congruent.