Download Conditional Notes

Conditional (If-Then) Statements
Every conditional statement has a
hypothesis (IF) and a conclusion
(THEN).
Example:
If you work hard, then you will pass this
class.
Hypothesis: You work hard.
Conclusion: You will pass this class.
Notice the words “if” and “then” are
NOT part of the wording of the
hypothesis and conclusion.
Identify the hypothesis and conclusion:
If two lines intersect, then they intersect
in exactly one point.
Write each sentence as a conditional:
An acute angle measures less than 900.
If an angle is acute, then it measures less
than 900.
Three noncollinear points are contained
in exactly one plane.
If three points are noncollinear, then they
are contained in exactly one plane.
Writing the Converse of a Conditional:
The converse of a conditional switches
the hypothesis and the conclusion.
Example:
Conditional: If the figure has four sides,
then it is a quadrilateral.
Converse: If a figure is a quadrilateral,
then it has four sides.
Try This:
If two lines intersect to form right angles,
then they are perpendicular.
If two lines are perpendicular, then they
intersect to form right angles.
Determining Truth Value:
To show that a conditional is TRUE,
every time the hypothesis is true, the
conclusion is also true.
To show that a conditional is FALSE, all
you need to do is find counterexample
for which the hypothesis is true and the
conclusion is false.
Example:
If two lines are parallel, then they do not
intersect.
(TRUE)
Converse:
If two lines do not intersect, then they
are parallel.
(FALSE – counterexample?)
Writing a Biconditional:
A biconditional is the statement formed
when you connect a conditional and its
converse and both are true.
Example:
If an angle is a straight angle, then its
measure is 1800.
If the measure of an angle is 1800, then it
is a straight angle.
An angle is a straight angle IF AND
ONLY IF its measure is 1800.