1. 2.2 Definitions and Biconditional Statements
Recall: A definition uses known words to describe a new word.
Perpendicular Lines ( ): Two lines that intersect to form a right angle.
A line perpendicular to a plane: A line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it. T m n T
n m { n P T
n P

2. Biconditional Statements
Biconditional: When a conditional and its converse are both true they can be combined into one statement using “if and only if” (iff).
Writing a biconditional statement is equivalent to writing a conditional and its converse.
If an angle is a right angle, then its measure is 90.
Converse: If the measure of an angle is 90, then it is a right angle.
Are both of these statements true?
An angle is a right angle if and only if its measure is 90.

3. Rewriting a Biconditional Statement
Biconditionals can be rewritten as a conditional and its converse.
Three lines are coplanar if and only if they lie in the same plane.
Conditional: If three lines are coplanar, then they lie in the same plane.
Converse: If three lines lie in the same plane, then they are coplanar.
Analyze the following statement.
x = 3 if and only if x2 = 9.
Is this a biconditional statement?
Is the statement true?

4. Knowing how to use true biconditional statements is an important tool for geometry. If you can write a biconditional statement that is true then you can use the conditional statement or its converse to justify an argument.
Can the Segment Addition Postulate be written as a biconditional statement?
If B lies between A and C, then
AB + BC = AC.
Converse:
Point B lies between points A and C if and only if AB + BC = AC.