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2.1 Conditional StatementsMrs. SpitzGeometryFall 2005
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Standards/Objectives:Students will learn and apply geometric
concepts.Objectives:Recognize and analyze a conditional
statementWrite postulates about points, lines, and planes using
conditional statements.
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Assignment:Pp. 75-77 #4-28 all, 46-49 all.
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Conditional StatementA logical statement with 2 parts2 parts are
called the hypothesis & conclusionCan be written in if-then
form; such as, If, then
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Conditional StatementHypothesis is the part after the word
IfConclusion is the part after the word then
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Ex: Underline the hypothesis & circle the conclusion.If you
are a brunette, then you have brown hair.
hypothesisconclusion
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Ex: Rewrite the statement in if-then formVertical angles are
congruent.If there are 2 vertical angles, then they are
congruent.If 2 angles are vertical, then they are congruent.
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Ex: Rewrite the statement in if-then formAn object weighs one
ton if it weighs 2000 lbs.If an object weighs 2000 lbs, then it
weighs one ton.
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CounterexampleUsed to show a conditional statement is false.It
must keep the hypothesis true, but the conclusion false!It must
keep the hypothesis true, but the conclusion false!It must keep the
hypothesis true, but the conclusion false!
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Ex: Find a counterexample to prove the statement is false.If
x2=81, then x must equal 9.counterexample: x could be -9because
(-9)2=81, but x9.
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NegationWriting the opposite of a statement.
Ex: negate x=3x3Ex: negate t>5t 5
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ConverseSwitch the hypothesis & conclusion parts of a
conditional statement.
Ex: Write the converse of If you are a brunette, then you have
brown hair.If you have brown hair, then you are a brunette.
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InverseNegate the hypothesis & conclusion of a conditional
statement.
Ex: Write the inverse of If you are a brunette, then you have
brown hair.If you are not a brunette, then you do not have brown
hair.
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ContrapositiveNegate, then switch the hypothesis &
conclusion of a conditional statement.
Ex: Write the contrapositive of If you are a brunette, then you
have brown hair.If you do not have brown hair, then you are not a
brunette.
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The original conditional statement & its contrapositive will
always have the same meaning.
The converse & inverse of a conditional statement will
always have the same meaning.
