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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.
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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. BECOMES If Keanu Reaves isn’t acting, then he isn’t playing a confused idiot.
CONDITIONAL STATEMENTS • Finally, the contrapositiveof 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. • Biconditionalsuse 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.
