Conditional Statements Conditional Statement: “If, then” format. Converse: “Flipping the Logic” –Still “if, then” format, but we switch the hypothesis.

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Conditional Statements Conditional Statement: “If, then” format. Converse: “Flipping the Logic” –Still “if, then” format, but we switch the hypothesis and conclusion Negation: We can alter a statement by converting it to it’s negative form. –Inverse: Negating the hypothesis and conclusion of the original conditional statement –Contra-positive: Negating the hypothesis and conclusion of the of the Converse Equivalent Statements: When two statements are both true or both false. –A Conditional statement is equivalent to it’s contra-positive –Similarly, an inverse and converse of any conditional statement will be equivalent.

Equivalent Statements Equivalent Statements: When two statements are both true or both false. –A Conditional statement is equivalent to it’s contra-positive –Similarly, an inverse and converse of any conditional statement will be equivalent. Examples: –Conditional: If an angle measures 30, then it is an acute angle. (True) –Converse: If an angle is an acute angle, then it measures 30. (False) –Inverse: If an angle does not measure 30, then it is not acute. (False) –Contra-Positive: If an angle is not an acute angle, then it does not measure 30. (True)

Point, Line, and Plane Postulates Postulate 5: Through any 2 points there exists exactly one line. Postulate 6: A line contains at least 2 points. Postulate 7: If 2 lines intersect, then their intersection is exactly one point. Postulate 8: Through any 3 non-collinear points there exists exactly one plane. Postulate 9: A plane contains at least 3 non-collinear points. Postulate 10: If 2 points lie in a plane, then the line containing them lies in the plane. Postulate 11: If 2 planes intersect, then their intersection is a line.

Bi-conditional Statements Statements using the “if and only if” logic construct –In other words, the conclusion can only be true, “if and only if” the hypothesis holds. Again – simply because the logic holds, does not make the bi-conditional stmt true Testing the logic: –Re-write the bi-conditional as: A conditional statement, And it’s converse –If BOTH are true, the bi-conditional is true.