Conditional Statements
A statement written in theif-thenform is a conditional statement.
represents the conditional statement
“ifthen.”
Example 1:
If two angles areadjacent, then they have a common side.
The part of the statement followingifis called thehypothesis, and the part followingthenis called the conclusion.
Example 2:
Identify the hypothesis and conclusion of the following statement.
Apolygonis 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 theif and only ifform.
Two line segments are congruentif and only ifthey 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 symbolor.
means thatand. That is,.
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.