LESSON THREE:
IF I HATE THIS MOVIE…
CONDITIONAL STATEMENTS
• Mathematical statements in the if-then form
are called conditional statements.
CONDITIONAL STATEMENTS
• The if part is called the hypothesis.
• The then part is called the conclusion.
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CONDITIONAL STATEMENTS
• So, label the statement…
• If I hate this movie, then I will drive to
Hollywood and punch out the director.
• The hypothesis is I hate this movie.
• The conclusion is I will drive to Hollywood
and punch out the director.
CONDITIONAL STATEMENTS
• The challenge comes in the rearrangements of
conditionals.
• A converse just the reverse of an original
statement.
• If a movie is on its fifth sequel, then it will be bad.
BECOMES
If a movie is bad, then it is on its fifth sequel.
CONDITIONAL STATEMENTS
• An inverse is formed of the negations of the
hypothesis and conclusion.
• If Keanu Reaves is acting, then he is playing a
confused idiot.
BECOMES
If Keanu Reaves isn’t acting, then he isn’t
playing a confused idiot.
CONDITIONAL STATEMENTS
• Finally, the contrapositive of a conditional is
the interchanged negation of the original.
• If Adam Sandler stars in a movie, then the
movie will be loud and obnoxious.
BECOMES
If a movie isn’t loud and obnoxious, then
Adam Sandler doesn’t star in the movie.
CONDITIONAL STATEMENTS
• Conditionals will be very important when we
begin working with proofs.
• Biconditionals use the phrase “if and only if”.
• Let’s use the IFF notation to find a definition
for “midpoint”.
CONDITIONAL STATEMENTS
• Certain things in Geometry have undefined
explanations.
CONDITIONAL STATEMENTS
• Examples include…
– Points: Have NO size.
– Lines: Have NO thickness.
• A new term with an undefined explanation is a
plane.
– These also have no thickness, but they do have
two-dimensions.
CONDITIONAL STATEMENTS
• Points that lie on the same plane are called
coplanar.
POSTULATES WORTH KNOWING
• Straight-Line Postulate – Two points are
contained on one and only one line. (Two
points determine a line).
B
A
POSTULATES WORTH KNOWING
• Plane Postulate – Three noncollinear points
are contained in one and only one plane.
(Three noncollinear points determine a plane.)
POSTULATES WORTH KNOWING
• Flat-Plane Postulate – If two points are in a
plane, then the line containing the points is in
the same plane.
POSTULATES WORTH KNOWING
• Plane-Intersection Postulate – If two planes
intersect, then their intersections is a line.