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.
If AM=MB, then M is the midpoint of AB.
2. If |x| = 6, then x = 6 or x = -6.
If x = 6 or x = -6, then |x| = 6
3. You score a goal if the ball crosses the goal line.
If you score a goal, then 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
If x = 4 then x2 = 16
If x2 = 16 then x = 4
Point Y lies between X and Z if and only if XY + YZ = XZ
If point Y lies between X and Z then XY + YZ = XZ
If XY + YZ = XZ then point Y lies between X and Z
The car will run if and only if there is gas in the tank
If the car will run then there is gas in the tank
If there is gas in the tank then the car will run

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

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
If you are a teenager, then you are 15 years old
FALSE
If point C is on Ray BA, then point C is on line BA
If point C is on line BA then point C is on Ray BA
False

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
If two angles have a sum of 90 then they are complementary (TRUE)
Two angles are complementary if and only if their sum is 90.
If point C is between A and B, then Ray CA and Ray CB are opposite rays
If ray CA and Ray CB are opposite rays then point C is between A and B (TRUE)
Point C is between A and B if and only if ray CA and ray CB are opposite rays

10. If two angles form a linear pair then they are adjacent
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
If two angles are adjacent then they forma linear pair
False

11. Write a definition of an E-flat baritone saxophone
A saxophone that has a frequency of 69 cycles per second to 416 cycles per second is called an E-Flat baritone sax
Tell whether the following conditional is true, if not explain why.
If a note played on a saxophone has a frequency of 610 cycles per second then the saxophone is an E-flat alto saxophone
False: It could be a B-flat tenor saxophone