1. Section 2.2 Definitions and Biconditionals
Chapter 2
Section 2.2
Definitions and Biconditionals

2. Warm-Up Write the converse of each statement.
If M is the midpoint of AB, then AM=MB.
2. If |x| = 6, then x = 6 or x = -6.
3. You score a goal if the ball crosses the goal line.

3. Perpendicular
Two lines are perpendicular if they intersect to form a right angle.
A line is perpendicular to a plane if it intersects the plane and is perpendicular to every line in the plane. l m
l  m

4. Use the diagram to determine if the statement is true or false

5. Biconditional A statement that contains the words “if and only if”
A biconditional is equivalent to writing a conditional statement and its converse
Example: 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
The biconditional means BOTH the conditional and its converse are TRUE

6. Rewrite each biconditional statement as a conditional and its converse
x = 4 if and only if x2 = 16
1. Conditional
2. Converse
9. Point Y lies between X and Z if and only if XY + YZ = XZ 1. 2.
The car will run if and only if there is gas in the tank

7. Rewrite each biconditional statement as a conditional and its converse
Two angles are congruent if and only if they have the same measure 1. 2.
12. An angle is a right angle if and only if it measures 90

8. Write the converse of each true statement
Write the converse of each true statement. If it is true combine them to write a true biconditional
If you are 15 years old then you are a teenager 1. 2.
14. If point C is on Ray BA, then point C is on line BA

9. Write the converse of each true statement
Write the converse of each true statement. If it is true combine them to write a true biconditional
If two angles are complementary then the sum of their measures is 90 1. 2.
If point C is between A and B, then Ray CA and Ray CB are opposite rays

10. If two angles form a linear pair then they are adjacent 1. 2.
Write the converse of each true statement. If it is true combine them to write a true biconditional
If two angles form a linear pair then they are adjacent 1. 2.

11. Write a definition of an E-flat baritone saxophone
Tell whether the following conditional is true, if not explain why.