Section 2-2
Biconditional
Statements
Biconditional statement
• a statement that contains
the phrase “if and only if”.
• Equivalent to a conditional
statement and its converse.
We can use
iff to stand
for “If and
only if”
In order for a
biconditional
statement to be
TRUE, both the
conditional statement
and its converse must
be true.
Example #1:
Write this biconditional statement
as a conditional statement.
• Two lines intersect if and
only if their intersection is
exactly one point.
Conditional Statement:
• If two lines intersect, then
their intersection is exactly
one point. True
Now write the converse.
• If their intersection is exactly
one point, then two lines
intersect. True
Example #2
Write this biconditional statement
as a conditional statement.
• Three lines are coplanar
if and only if they lie in
the same plane.
Conditional Statement:
•If three lines are coplanar,
then they lie in the same
plane. True
Now write the converse.
•If three lines lie in the
same plane, then they are
coplanar. True
Write the conditional as a
biconditional statement.
• If an angle is acute then
it has a measure
between 0° and 90°.
Write the converse
• If an angle has a
measure between 0° and
90°, then it is acute. True
Identify whether the
converse is true or false
• If it is true, then a
biconditional can be written
• If it is false, then a
biconditional CAN NOT be
written.
Bicondtional:
• An angle is acute if and
only if it has a measure
between 0° and 90°.
Write the conditional as a
biconditional statement.
• If an animal is a leopard,
then it has spots.
Write the converse.
• If an animal has spots, then
is a leopard. False
Therefore a
biconditional for
this statement
does not exist!
More Examples:
Try It!
Write each conditional as a
biconditional statement, if
possible. Be sure to give a
counterexample if the converse
is false!
1.If SR is perpendicular to QR ,
then their intersection forms
a right angle.
Converse:
If, SR and QR intersect at a
right angle, then they are
perpendicular to each other.
True
Biconditional:
• SR is perpendicular to QR
iff their intersection forms
a right angle.
2. If
2
x <
49, then x < 7
Converse:
2
If x < 7, then x < 49.
• Counterexample:
2
let x  8 then  8  49
Therefore, a biconditional
can not be written!