lesson three: if i hate this movie…
DESCRIPTION
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. =. CONDITIONAL STATEMENTS. - PowerPoint PPT PresentationTRANSCRIPT
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.
=
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.
BECOMESIf 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.
BECOMESIf 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).
A
B
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.