1. Section 2.2 Definitions and Biconditional Statement

2. Definition of Perpendicular Lines
Two lines that intersect to form a right angle.

3. Definition of 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.

4. Definitions are Forward and Backward
All definitions can be interpreted “forward” and “backward.”
If two lines are perpendicular, then they intersect to form a right angle OR
If two lines intersect to form a right angle, then they are perpendicular.

5. Biconditional Statements
Not all conditional statements are written in the If-Then form. Biconditional statements are conditional statements too.
A biconditional statement contains the phrase, “if and only if” OR “iff”
Ex. 1 The light is on if and only if the light switch is up.

6. Biconditional Statement (continued-)
Writing a biconditional statement is equivalent to writing a conditional statement and its converse.
If-then Cond. State. (forward)
If the light is on, then the light switch is up.
Converse (backward)
If the light switch is up, then the light is on.

7. Facts on Biconditional Statements
Biconditional statements can be either TRUE or FALSE.
To be TRUE, BOTH the conditional statement and its converse must be true.
Therefore, ALL true biconditional statements are True both forward and backward.
All definitions can be written as true biconditional statements.

8. Why are Biconditional Statements Important?
If you can write a true biconditional statement, then you can use the conditional statement- “If-Then” or the converse to justify an argument.