Transcript Geometry Chapter 1 – The Basics of Geometry

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:
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–
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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.