2.2 Biconditionals and
Definitions
Two cards
Biconditionals
When a conditional and its converse
are true, then you can combine them
as a biconditional.
Use the words:
“if and only if”
Ex 1: Write as a Biconditional
Conditional:
If an angle measures 90 degrees, then
it is a right angle.
Converse: If an angle is a right angle,
then it measures 90 degrees.
Both are True.
Ex 1: Write as a Biconditional
Long way:
If an angle measures 90 degrees, then
it is a right angle AND if an angle is a
right angle, then it measures 90
degrees.
Short Way:
An angle measures 90 degrees IF AND
ONLY IF it is a right angle
Ex 1: Write as a Biconditional
Conditional:
If three points are collinear, then they
lie on the same line.
Converse:
True or False?
If True, Write it as a Biconditional
Ex 1: Write as a Biconditional
Conditional:
If three points are collinear, then they
lie on the same line.
Converse:
If three points line on the same line,
then they are collinear.
True
Three points are collinear IF AND ONLY
IF they lie on the same line.
Ex 1: Write as a Biconditional
Conditional:
If x = 5 then x + 15 = 20
Converse:
True or False?
If True, Write it as a Biconditional
Ex 1: Write as a Biconditional
Conditional:
If x = 5 then x + 15 = 20
Converse:
If x + 15 = 20, then x = 5
True
Biconditional:
X = 5 IF AND ONLY IF x + 15 = 20
Ex 2: Separate a Biconditional
Biconditional:
A number is divisible by 3 if and only if
the sum of the digits is divisible by 3.
Ex 2: Separate a Biconditional
Two converse statements:
If a number is divisible by 3, then the
sum of the digits is divisible by 3.
If the sum of the digits is divisible by
3, then a number is divisible by 3.
Ex 2: Separate a Biconditional
Biconditional:
A number is prime if and only if it only
has two distinct factors, 1 and itself.
Ex 2: Separate a Biconditional
Two converse statements:
If a number is prime, then it only has
two distinct factors, 1 and itself.
If a number has two distinct factors, 1
and itself, then it is prime.
Summary
Biconditional:
A
B
Good Definitions




Helps to identify or classify an object
Uses clearly understood terms
Is precise (avoids words like large,
sort of and some)
Is reversible (can be written as a true
biconditional statement)
Definitions
Is it reversible? If so, write it as a true
biconditional:
Definition:
A right angle is an angle whose
measure is 90 degrees.
Definitions
Yes It is reversible:
Conditional:
If an angle is a right angle, then it
measure is 90 degrees.
Converse:
If an angle measures 90 degrees, then
it is a right angle.
Biconditional:
An angle is right if and only if it
measures 90 degrees.
Definitions
Good or Bad?


Perpendicular lines are two lines that
intersect to form right angles.
Parallel lines are two lines that are
sort of close to each other.
Definitions
Good or Bad?
Perpendicular lines are two lines that
intersect to form right angles.
Good – Can write it biconditionally
 Parallel lines are two lines that are
sort of close to each other.
Bad – Lines that are close to each
other might intersect eventually.

Definitions
Good or Bad?

An airplane is a vehicle that flies.

A triangle has sharp corners.

A square is a figure with four right
angles.
Definitions
Good or Bad?
An airplane is a vehicle that flies.
Bad- a helicopter is a vehicle that flies
 A triangle has sharp corners.
Bad- sharp is an imprecise word
 A square is a figure with four right
angles.
Bad- A rectangle has four right angles

Homework
2.2 Pg 78