2.2 Conditional Statements.notebook
September 12, 2016
txt.pg.77 #11-13, 16-22
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2.2 Conditional Statements.notebook
September 12, 2016
What we will learn today:
• Analyze the truth value of a conditional
statement,
• Write the inverse, converse, and
contrapositive of a conditional
statement
Often times in advertising we hear...
“If you are not 100% satisfied with this
product, then return it for a full refund of
the purchase price.”
Conditional statements have two parts.
• The hypothesis (p) is the part following the if.
• The conclusion (q) is the part following the then.
Examples ~ Write each conditional statement
if-then form.
(1) Two angles are congruent if they have the
same measures.
in
(2) We will cancel practice if it rains tonight.
(3) Points that lie on the same line are collinear.
(4) Two angles that are complementary are acute.
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2.2 Conditional Statements.notebook
September 12, 2016
Writing the converse of a conditional statement
Original statement: p --> q
Converse: q --> p
The converse of a conditional statement is formed by
exchanging the hypothesis and conclusion of a
conditional.
Conditional: If a figure is a triangle, then it has three angles
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
Conditional: If it isn't raining , then I will walk home
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
Conditional: If the Steelers win, then Mrs. Hansen is happy
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
Conditional: If two planes intersect , then a line is formed
Hypothesis:
Conclusion:
Converse: If ____________________, then _________________.
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2.2 Conditional Statements.notebook
September 12, 2016
Determine whether a converse is true or false
Just because the original statement is true,
does not mean its converse is true.
When false, we must provide a
counterexample.
Examples ~ Write the converse of each true
conditional statement. Determine whether each
converse is true or false. If false, give a
counterexample.
(a) Mrs. Kronberger is happy if the Steelers win.
(b) If angles are acut, they have measures less than 90.
(c) Vertical angles are congruent.
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2.2 Conditional Statements.notebook
September 12, 2016
The converse, inverse, and contrapositive of
a conditional statement
Original If-Then statement:
Converse :
Inverse:
Contrapositive:
Examples
(1) p --> q: If two angles are vertical angles, then
they are congruent.
converse (q --> p):
inverse (~p --> ~q):
contrapositive (~q --> ~p):
(2) If two angles are complementary, then the
sum of their measures is 90o .
converse:
inverse:
contrapositive:
(3) If points are coplanar, then they lie in the
same plane.
converse:
inverse:
contrapositive:
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