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.

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.