A statement written in the if-then form is a conditional statement.
represents the conditional statement
“if then .”
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.
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.
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 .
means that and . That is, .
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.